family stringclasses 1 value | question_id int64 0 2 | signal_type stringclasses 2 values | amplitude_scale float64 0.5 2.5 | frequency_cycles float64 1 16 | phase_deg float64 0 240 ⌀ | time_step int64 0 255 | p_value float64 3.5 4.5 | prompt stringlengths 59 76 | ground_truth float64 0.52 2.33 | symbolic_baseline_answer float64 0.52 2.33 |
|---|---|---|---|---|---|---|---|---|---|---|
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 0 | 4 | Solve this system for x:
4.0x + 1y = 7
1x + 5y = 11
FINAL: | 1.263158 | 1.263158 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 1 | 4.009802 | Solve this system for x:
4.009801714032956x + 1y = 7
1x + 5y = 11
FINAL: | 1.259908 | 1.259908 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 2 | 4.019509 | Solve this system for x:
4.019509032201613x + 1y = 7
1x + 5y = 11
FINAL: | 1.256706 | 1.256706 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 3 | 4.029028 | Solve this system for x:
4.029028467725446x + 1y = 7
1x + 5y = 11
FINAL: | 1.253582 | 1.253582 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 4 | 4.038268 | Solve this system for x:
4.038268343236509x + 1y = 7
1x + 5y = 11
FINAL: | 1.250564 | 1.250564 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 5 | 4.04714 | Solve this system for x:
4.0471396736826x + 1y = 7
1x + 5y = 11
FINAL: | 1.24768 | 1.24768 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 6 | 4.055557 | Solve this system for x:
4.05555702330196x + 1y = 7
1x + 5y = 11
FINAL: | 1.244956 | 1.244956 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 7 | 4.063439 | Solve this system for x:
4.063439328416364x + 1y = 7
1x + 5y = 11
FINAL: | 1.242416 | 1.242416 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 8 | 4.070711 | Solve this system for x:
4.070710678118655x + 1y = 7
1x + 5y = 11
FINAL: | 1.240082 | 1.240082 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 9 | 4.077301 | Solve this system for x:
4.077301045336274x + 1y = 7
1x + 5y = 11
FINAL: | 1.237975 | 1.237975 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 10 | 4.083147 | Solve this system for x:
4.083146961230255x + 1y = 7
1x + 5y = 11
FINAL: | 1.236111 | 1.236111 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 11 | 4.088192 | Solve this system for x:
4.088192126434835x + 1y = 7
1x + 5y = 11
FINAL: | 1.234507 | 1.234507 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 12 | 4.092388 | Solve this system for x:
4.092387953251128x + 1y = 7
1x + 5y = 11
FINAL: | 1.233176 | 1.233176 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 13 | 4.095694 | Solve this system for x:
4.095694033573221x + 1y = 7
1x + 5y = 11
FINAL: | 1.23213 | 1.23213 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 14 | 4.098079 | Solve this system for x:
4.098078528040323x + 1y = 7
1x + 5y = 11
FINAL: | 1.231376 | 1.231376 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 15 | 4.099518 | Solve this system for x:
4.09951847266722x + 1y = 7
1x + 5y = 11
FINAL: | 1.230921 | 1.230921 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 16 | 4.1 | Solve this system for x:
4.1x + 1y = 7
1x + 5y = 11
FINAL: | 1.230769 | 1.230769 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 17 | 4.099518 | Solve this system for x:
4.09951847266722x + 1y = 7
1x + 5y = 11
FINAL: | 1.230921 | 1.230921 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 18 | 4.098079 | Solve this system for x:
4.098078528040323x + 1y = 7
1x + 5y = 11
FINAL: | 1.231376 | 1.231376 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 19 | 4.095694 | Solve this system for x:
4.095694033573221x + 1y = 7
1x + 5y = 11
FINAL: | 1.23213 | 1.23213 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 20 | 4.092388 | Solve this system for x:
4.092387953251128x + 1y = 7
1x + 5y = 11
FINAL: | 1.233176 | 1.233176 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 21 | 4.088192 | Solve this system for x:
4.088192126434835x + 1y = 7
1x + 5y = 11
FINAL: | 1.234507 | 1.234507 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 22 | 4.083147 | Solve this system for x:
4.083146961230255x + 1y = 7
1x + 5y = 11
FINAL: | 1.236111 | 1.236111 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 23 | 4.077301 | Solve this system for x:
4.077301045336274x + 1y = 7
1x + 5y = 11
FINAL: | 1.237975 | 1.237975 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 24 | 4.070711 | Solve this system for x:
4.070710678118655x + 1y = 7
1x + 5y = 11
FINAL: | 1.240082 | 1.240082 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 25 | 4.063439 | Solve this system for x:
4.063439328416364x + 1y = 7
1x + 5y = 11
FINAL: | 1.242416 | 1.242416 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 26 | 4.055557 | Solve this system for x:
4.05555702330196x + 1y = 7
1x + 5y = 11
FINAL: | 1.244956 | 1.244956 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 27 | 4.04714 | Solve this system for x:
4.0471396736826x + 1y = 7
1x + 5y = 11
FINAL: | 1.24768 | 1.24768 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 28 | 4.038268 | Solve this system for x:
4.038268343236509x + 1y = 7
1x + 5y = 11
FINAL: | 1.250564 | 1.250564 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 29 | 4.029028 | Solve this system for x:
4.029028467725446x + 1y = 7
1x + 5y = 11
FINAL: | 1.253582 | 1.253582 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 30 | 4.019509 | Solve this system for x:
4.019509032201613x + 1y = 7
1x + 5y = 11
FINAL: | 1.256706 | 1.256706 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 31 | 4.009802 | Solve this system for x:
4.009801714032956x + 1y = 7
1x + 5y = 11
FINAL: | 1.259908 | 1.259908 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 32 | 4 | Solve this system for x:
4.0x + 1y = 7
1x + 5y = 11
FINAL: | 1.263158 | 1.263158 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 33 | 3.990198 | Solve this system for x:
3.9901982859670437x + 1y = 7
1x + 5y = 11
FINAL: | 1.266425 | 1.266425 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 34 | 3.980491 | Solve this system for x:
3.9804909677983873x + 1y = 7
1x + 5y = 11
FINAL: | 1.269676 | 1.269676 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 35 | 3.970972 | Solve this system for x:
3.970971532274554x + 1y = 7
1x + 5y = 11
FINAL: | 1.272882 | 1.272882 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 36 | 3.961732 | Solve this system for x:
3.961731656763491x + 1y = 7
1x + 5y = 11
FINAL: | 1.276008 | 1.276008 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 37 | 3.95286 | Solve this system for x:
3.9528603263174x + 1y = 7
1x + 5y = 11
FINAL: | 1.279024 | 1.279024 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 38 | 3.944443 | Solve this system for x:
3.94444297669804x + 1y = 7
1x + 5y = 11
FINAL: | 1.2819 | 1.2819 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 39 | 3.936561 | Solve this system for x:
3.9365606715836354x + 1y = 7
1x + 5y = 11
FINAL: | 1.284604 | 1.284604 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 40 | 3.929289 | Solve this system for x:
3.9292893218813454x + 1y = 7
1x + 5y = 11
FINAL: | 1.287109 | 1.287109 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 41 | 3.922699 | Solve this system for x:
3.9226989546637263x + 1y = 7
1x + 5y = 11
FINAL: | 1.289387 | 1.289387 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 42 | 3.916853 | Solve this system for x:
3.9168530387697453x + 1y = 7
1x + 5y = 11
FINAL: | 1.291415 | 1.291415 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 43 | 3.911808 | Solve this system for x:
3.9118078735651647x + 1y = 7
1x + 5y = 11
FINAL: | 1.29317 | 1.29317 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 44 | 3.907612 | Solve this system for x:
3.9076120467488713x + 1y = 7
1x + 5y = 11
FINAL: | 1.294634 | 1.294634 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 45 | 3.904306 | Solve this system for x:
3.904305966426779x + 1y = 7
1x + 5y = 11
FINAL: | 1.295789 | 1.295789 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 46 | 3.901921 | Solve this system for x:
3.901921471959677x + 1y = 7
1x + 5y = 11
FINAL: | 1.296624 | 1.296624 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 47 | 3.900482 | Solve this system for x:
3.90048152733278x + 1y = 7
1x + 5y = 11
FINAL: | 1.297128 | 1.297128 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 48 | 3.9 | Solve this system for x:
3.9x + 1y = 7
1x + 5y = 11
FINAL: | 1.297297 | 1.297297 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 49 | 3.900482 | Solve this system for x:
3.90048152733278x + 1y = 7
1x + 5y = 11
FINAL: | 1.297128 | 1.297128 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 50 | 3.901921 | Solve this system for x:
3.901921471959677x + 1y = 7
1x + 5y = 11
FINAL: | 1.296624 | 1.296624 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 51 | 3.904306 | Solve this system for x:
3.904305966426779x + 1y = 7
1x + 5y = 11
FINAL: | 1.295789 | 1.295789 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 52 | 3.907612 | Solve this system for x:
3.9076120467488713x + 1y = 7
1x + 5y = 11
FINAL: | 1.294634 | 1.294634 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 53 | 3.911808 | Solve this system for x:
3.9118078735651647x + 1y = 7
1x + 5y = 11
FINAL: | 1.29317 | 1.29317 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 54 | 3.916853 | Solve this system for x:
3.9168530387697453x + 1y = 7
1x + 5y = 11
FINAL: | 1.291415 | 1.291415 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 55 | 3.922699 | Solve this system for x:
3.9226989546637263x + 1y = 7
1x + 5y = 11
FINAL: | 1.289387 | 1.289387 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 56 | 3.929289 | Solve this system for x:
3.9292893218813454x + 1y = 7
1x + 5y = 11
FINAL: | 1.287109 | 1.287109 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 57 | 3.936561 | Solve this system for x:
3.9365606715836354x + 1y = 7
1x + 5y = 11
FINAL: | 1.284604 | 1.284604 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 58 | 3.944443 | Solve this system for x:
3.94444297669804x + 1y = 7
1x + 5y = 11
FINAL: | 1.2819 | 1.2819 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 59 | 3.95286 | Solve this system for x:
3.9528603263174x + 1y = 7
1x + 5y = 11
FINAL: | 1.279024 | 1.279024 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 60 | 3.961732 | Solve this system for x:
3.961731656763491x + 1y = 7
1x + 5y = 11
FINAL: | 1.276008 | 1.276008 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 61 | 3.970972 | Solve this system for x:
3.970971532274554x + 1y = 7
1x + 5y = 11
FINAL: | 1.272882 | 1.272882 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 62 | 3.980491 | Solve this system for x:
3.9804909677983873x + 1y = 7
1x + 5y = 11
FINAL: | 1.269676 | 1.269676 |
linear_system | 0 | sinusoid | 0.5 | 1 | 0 | 63 | 3.990198 | Solve this system for x:
3.9901982859670437x + 1y = 7
1x + 5y = 11
FINAL: | 1.266425 | 1.266425 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 0 | 4 | Solve this system for x:
4.0x + 1y = 7
1x + 5y = 11
FINAL: | 1.263158 | 1.263158 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 1 | 4.019509 | Solve this system for x:
4.019509032201613x + 1y = 7
1x + 5y = 11
FINAL: | 1.256706 | 1.256706 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 2 | 4.038268 | Solve this system for x:
4.038268343236509x + 1y = 7
1x + 5y = 11
FINAL: | 1.250564 | 1.250564 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 3 | 4.055557 | Solve this system for x:
4.05555702330196x + 1y = 7
1x + 5y = 11
FINAL: | 1.244956 | 1.244956 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 4 | 4.070711 | Solve this system for x:
4.070710678118655x + 1y = 7
1x + 5y = 11
FINAL: | 1.240082 | 1.240082 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 5 | 4.083147 | Solve this system for x:
4.083146961230255x + 1y = 7
1x + 5y = 11
FINAL: | 1.236111 | 1.236111 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 6 | 4.092388 | Solve this system for x:
4.092387953251128x + 1y = 7
1x + 5y = 11
FINAL: | 1.233176 | 1.233176 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 7 | 4.098079 | Solve this system for x:
4.098078528040323x + 1y = 7
1x + 5y = 11
FINAL: | 1.231376 | 1.231376 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 8 | 4.1 | Solve this system for x:
4.1x + 1y = 7
1x + 5y = 11
FINAL: | 1.230769 | 1.230769 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 9 | 4.098079 | Solve this system for x:
4.098078528040323x + 1y = 7
1x + 5y = 11
FINAL: | 1.231376 | 1.231376 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 10 | 4.092388 | Solve this system for x:
4.092387953251128x + 1y = 7
1x + 5y = 11
FINAL: | 1.233176 | 1.233176 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 11 | 4.083147 | Solve this system for x:
4.083146961230255x + 1y = 7
1x + 5y = 11
FINAL: | 1.236111 | 1.236111 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 12 | 4.070711 | Solve this system for x:
4.070710678118655x + 1y = 7
1x + 5y = 11
FINAL: | 1.240082 | 1.240082 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 13 | 4.055557 | Solve this system for x:
4.05555702330196x + 1y = 7
1x + 5y = 11
FINAL: | 1.244956 | 1.244956 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 14 | 4.038268 | Solve this system for x:
4.038268343236509x + 1y = 7
1x + 5y = 11
FINAL: | 1.250564 | 1.250564 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 15 | 4.019509 | Solve this system for x:
4.019509032201613x + 1y = 7
1x + 5y = 11
FINAL: | 1.256706 | 1.256706 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 16 | 4 | Solve this system for x:
4.0x + 1y = 7
1x + 5y = 11
FINAL: | 1.263158 | 1.263158 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 17 | 3.980491 | Solve this system for x:
3.9804909677983873x + 1y = 7
1x + 5y = 11
FINAL: | 1.269676 | 1.269676 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 18 | 3.961732 | Solve this system for x:
3.961731656763491x + 1y = 7
1x + 5y = 11
FINAL: | 1.276008 | 1.276008 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 19 | 3.944443 | Solve this system for x:
3.94444297669804x + 1y = 7
1x + 5y = 11
FINAL: | 1.2819 | 1.2819 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 20 | 3.929289 | Solve this system for x:
3.9292893218813454x + 1y = 7
1x + 5y = 11
FINAL: | 1.287109 | 1.287109 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 21 | 3.916853 | Solve this system for x:
3.9168530387697453x + 1y = 7
1x + 5y = 11
FINAL: | 1.291415 | 1.291415 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 22 | 3.907612 | Solve this system for x:
3.9076120467488713x + 1y = 7
1x + 5y = 11
FINAL: | 1.294634 | 1.294634 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 23 | 3.901921 | Solve this system for x:
3.901921471959677x + 1y = 7
1x + 5y = 11
FINAL: | 1.296624 | 1.296624 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 24 | 3.9 | Solve this system for x:
3.9x + 1y = 7
1x + 5y = 11
FINAL: | 1.297297 | 1.297297 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 25 | 3.901921 | Solve this system for x:
3.901921471959677x + 1y = 7
1x + 5y = 11
FINAL: | 1.296624 | 1.296624 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 26 | 3.907612 | Solve this system for x:
3.9076120467488713x + 1y = 7
1x + 5y = 11
FINAL: | 1.294634 | 1.294634 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 27 | 3.916853 | Solve this system for x:
3.9168530387697453x + 1y = 7
1x + 5y = 11
FINAL: | 1.291415 | 1.291415 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 28 | 3.929289 | Solve this system for x:
3.9292893218813454x + 1y = 7
1x + 5y = 11
FINAL: | 1.287109 | 1.287109 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 29 | 3.944443 | Solve this system for x:
3.94444297669804x + 1y = 7
1x + 5y = 11
FINAL: | 1.2819 | 1.2819 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 30 | 3.961732 | Solve this system for x:
3.961731656763491x + 1y = 7
1x + 5y = 11
FINAL: | 1.276008 | 1.276008 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 31 | 3.980491 | Solve this system for x:
3.9804909677983873x + 1y = 7
1x + 5y = 11
FINAL: | 1.269676 | 1.269676 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 32 | 4 | Solve this system for x:
4.0x + 1y = 7
1x + 5y = 11
FINAL: | 1.263158 | 1.263158 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 33 | 4.019509 | Solve this system for x:
4.019509032201613x + 1y = 7
1x + 5y = 11
FINAL: | 1.256706 | 1.256706 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 34 | 4.038268 | Solve this system for x:
4.038268343236509x + 1y = 7
1x + 5y = 11
FINAL: | 1.250564 | 1.250564 |
linear_system | 0 | sinusoid | 0.5 | 2 | 0 | 35 | 4.055557 | Solve this system for x:
4.05555702330196x + 1y = 7
1x + 5y = 11
FINAL: | 1.244956 | 1.244956 |
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