Time bar (total: 2.5m)
| 488.0ms | 1183× | body | 80 | nan |
| 216.0ms | 421× | body | 80 | valid |
| 347.0ms | (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) |
2 alts after pruning (2 fresh and 0 done)
Merged error: 24.8b
Found 4 expressions with local error:
| 11.9b | (sqrt (/ d h)) |
| 11.9b | (sqrt (/ d l)) |
| 8.1b | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h)))) |
| 6.8b | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 26× | sqrt-prod |
| 25× | add-sqr-sqrt |
| 20× | times-frac |
| 19× | *-un-lft-identity add-cube-cbrt |
| 11× | pow1 |
| 9× | add-cbrt-cube add-exp-log |
| 6× | sqrt-div |
| 4× | expm1-log1p-u rem-sqrt-square associate-*r/ insert-posit16 log1p-expm1-u add-log-exp |
| 3× | associate-*l* pow-prod-down prod-exp cbrt-unprod |
| 2× | sqrt-pow1 pow1/2 div-inv |
| 1× | frac-times associate-*r* associate-*l/ *-commutative fma-udef |
| 40.0ms | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h)))) |
| 11.0ms | (sqrt (/ d h)) |
| 4.0ms | (sqrt (/ d l)) |
| 0.0ms | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 540.0ms | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h)))) |
| 355.0ms | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 63.0ms | (sqrt (/ d h)) |
| 49.0ms | (sqrt (/ d l)) |
| 434.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (sqrt (/ d l)) (sqrt (/ d h))))) |
| 399.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h))))) (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h))))) |
| 333.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h))))) |
| 325.0ms | (- 1 (* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (* l (pow d 2))))) |
| 282.0ms | (- 1 (* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (* l (pow d 2))))) |
18 alts after pruning (18 fresh and 0 done)
Merged error: 13.1b
Found 4 expressions with local error:
| 11.9b | (sqrt (/ d l)) |
| 8.1b | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 6.8b | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 5.4b | (/ M (/ (* 2 d) D)) |
| 43× | times-frac |
| 31× | add-sqr-sqrt |
| 28× | *-un-lft-identity add-cube-cbrt |
| 22× | add-cbrt-cube add-exp-log |
| 14× | pow1 |
| 13× | sqrt-prod |
| 7× | associate-/r* prod-exp cbrt-unprod |
| 6× | pow-prod-down associate-*r/ div-inv |
| 5× | cbrt-undiv sqrt-div div-exp |
| 4× | expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp |
| 3× | associate-*l* associate-/l* |
| 2× | rem-sqrt-square |
| 1× | frac-times clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l/ associate-/r/ *-commutative fma-udef |
| 116.0ms | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 12.0ms | (/ M (/ (* 2 d) D)) |
| 2.0ms | (sqrt (/ d l)) |
| 0.0ms | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 867.0ms | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 384.0ms | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 59.0ms | (sqrt (/ d l)) |
| 38.0ms | (/ M (/ (* 2 d) D)) |
| 820.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 650.0ms | (* (sqrt (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 632.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (sqrt (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 610.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 562.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) |
25 alts after pruning (25 fresh and 0 done)
Merged error: 12.5b
Found 4 expressions with local error:
| 8.1b | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 6.8b | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 5.4b | (/ M (/ (* 2 d) D)) |
| 5.4b | (/ M (/ (* 2 d) D)) |
| 66× | times-frac |
| 40× | add-cbrt-cube add-exp-log |
| 37× | add-sqr-sqrt *-un-lft-identity add-cube-cbrt |
| 22× | pow1 |
| 15× | prod-exp cbrt-unprod |
| 14× | associate-/r* |
| 13× | pow-prod-down |
| 10× | cbrt-undiv div-exp div-inv |
| 8× | associate-*r/ |
| 6× | associate-/l* |
| 4× | expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp |
| 3× | associate-*l* |
| 2× | clear-num frac-2neg associate-/r/ |
| 1× | frac-times associate-*r* associate-*l/ *-commutative fma-udef |
| 199.0ms | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 7.0ms | (/ M (/ (* 2 d) D)) |
| 7.0ms | (/ M (/ (* 2 d) D)) |
| 0.0ms | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 1.6s | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 330.0ms | (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) |
| 46.0ms | (/ M (/ (* 2 d) D)) |
| 36.0ms | (/ M (/ (* 2 d) D)) |
| 1.5s | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 1.1s | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 925.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 915.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (sqrt (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 904.0ms | (* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (fabs (cbrt d))) (fabs (cbrt d))) (* (* (sqrt (/ (cbrt d) l)) (sqrt (/ (cbrt d) l))) (sqrt (/ (cbrt d) l)))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (sqrt (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h))))))) |
29 alts after pruning (29 fresh and 0 done)
Merged error: 10.8b
Found 4 expressions with local error:
| 10.2b | (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) |
| 8.1b | (* (fma (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 4.5b | (sqrt (/ (cbrt d) l)) |
| 4.4b | (/ (* M D) d) |
| 131× | add-cbrt-cube add-exp-log |
| 64× | prod-exp cbrt-unprod |
| 36× | cbrt-undiv div-exp |
| 35× | add-sqr-sqrt |
| 33× | times-frac |
| 28× | pow1 |
| 27× | *-un-lft-identity add-cube-cbrt |
| 22× | sqrt-prod |
| 16× | pow-prod-down |
| 14× | associate-*r* |
| 11× | associate-*r/ |
| 10× | cbrt-prod |
| 6× | frac-times associate-*l/ |
| 5× | sqrt-div |
| 4× | expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp |
| 3× | rem-sqrt-square associate-/r* div-inv |
| 2× | *-commutative unswap-sqr |
| 1× | clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l* |
| 207.0ms | (* (fma (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 106.0ms | (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) |
| 9.0ms | (/ (* M D) d) |
| 6.0ms | (sqrt (/ (cbrt d) l)) |
| 1.1s | (* (fma (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 221.0ms | (sqrt (/ (cbrt d) l)) |
| 100.0ms | (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) |
| 22.0ms | (/ (* M D) d) |
| 1.5s | (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d)) (* (* (/ (* M D) d) (/ (* M D) d)) (/ (* M D) d))) (/ (* (* h h) h) (* (* l l) l))) |
| 1.5s | (* (* (* (* (/ (* M D) d) (/ (* M D) d)) (/ (* M D) d)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d))) (/ (* (* h h) h) (* (* l l) l))) |
| 1.4s | (* (* (* (fma (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (fma (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) (* (fma (* (* (/ (* M D) d) (/ (* M D) d)) (/ h l)) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) |
| 1.4s | (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* d d) d))) (* (* (/ h l) (/ h l)) (/ h l))) |
| 1.4s | (* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* d d) d)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d))) (* (* (/ h l) (/ h l)) (/ h l))) |
35 alts after pruning (35 fresh and 0 done)
Merged error: 8.2b
30.4% (4.3b remaining)
Error of 11.6b against oracle of 7.2b and baseline of 13.4b
| 17.3s | 38146× | body | 80 | nan |
| 5.7s | 12695× | body | 80 | valid |