Details

Time bar (total: 2.0m)

sample1.1s

Algorithm
intervals
Results
834.0ms1220×body80nan
146.0ms401×body80valid

simplify384.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
384.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize64.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
11.8b
(sqrt (/ d h))
7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
24×add-sqr-sqrt
21×times-frac
18×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×sqrt-pow1 pow1/2 sqrt-div
1×clear-num associate-/r* frac-2neg fma-udef associate-/l*
Counts
4 → 91
Calls
4 calls:
Slowest
22.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (/ d l))
4.0ms
(sqrt (/ d h))
0.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series477.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
66.0ms
(sqrt (/ d h))
60.0ms
(sqrt (/ d l))
50.0ms
(/ (* M D) (* 2 d))

simplify8.1s

Counts
127 → 103
Calls
127 calls:
Slowest
611.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
456.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))
451.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
366.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))
322.0ms
(* (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))))

prune2.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize110.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))
6.8b
(/ (* M D) (* 2 d))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
28×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
13×sqrt-prod
12×times-frac
11×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp prod-exp cbrt-unprod
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×rem-sqrt-square clear-num associate-/r* frac-2neg associate-/l*
1×sqrt-pow1 pow1/2 sqrt-div fma-udef
Counts
4 → 87
Calls
4 calls:
Slowest
23.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
6.0ms
(sqrt (/ d l))
1.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series469.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
85.0ms
(sqrt (/ d l))
40.0ms
(/ (* M D) (* 2 d))
34.0ms
(/ (* M D) (* 2 d))

simplify11.3s

Counts
114 → 99
Calls
114 calls:
Slowest
701.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
662.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
498.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
444.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))
416.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))

prune2.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.2b

localize106.0ms

Local error

Found 4 expressions with local error:

7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))
6.8b
(/ (* M D) (* 2 d))
6.8b
(* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))

rewrite510.0ms

Algorithm
rewrite-expression-head
Rules
46×add-cbrt-cube add-exp-log
22×pow1
21×prod-exp cbrt-unprod
14×associate-*r/
13×pow-prod-down
12×sqrt-div
8×cbrt-undiv div-exp
5×add-sqr-sqrt frac-times *-un-lft-identity associate-*l/ add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
1×associate-*r* *-commutative fma-udef
Counts
4 → 96
Calls
4 calls:
Slowest
475.0ms
(* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
11.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
10.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
287.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
46.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))

simplify28.1s

Counts
111 → 108
Calls
111 calls:
Slowest
1.5s
(* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))) (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))))
1.1s
(* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (* (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ d (cbrt l)))) (sqrt (/ d (cbrt 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)))))))
1.1s
(* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (* (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))))
1.0s
(* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (* (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ d (cbrt l)))) (sqrt (/ d (cbrt 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)))))))
921.0ms
(* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (* (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt 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)))))))

prune3.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.3b

localize117.0ms

Local error

Found 4 expressions with local error:

7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))
6.8b
(/ (* M D) (* 2 d))
3.3b
(* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))

rewrite612.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
25×pow1
23×prod-exp cbrt-unprod
15×pow-prod-down
13×associate-*r/
12×sqrt-div
8×cbrt-undiv div-exp
5×frac-times associate-*l/
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
1×associate-*r* associate-*l* *-commutative fma-udef
Counts
4 → 97
Calls
4 calls:
Slowest
564.0ms
(* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))
22.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
1.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))
314.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
32.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify28.4s

Counts
115 → 109
Calls
115 calls:
Slowest
1.4s
(* (* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ d (cbrt l)))) (sqrt (/ d (cbrt 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))))))
1.2s
(* (* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
1.1s
(* (* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))))) (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt 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))))))
1.0s
(* (* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)) (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ d (cbrt l)))) (sqrt (/ d (cbrt 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))))))
991.0ms
(* (* (* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))))) (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt 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))))))

prune2.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.9b

regimes1.6s

Accuracy

31.6% (2.6b remaining)

Error of 13.4b against oracle of 10.8b and baseline of 14.6b

bsearch993.0ms

end0.0ms

sample23.1s

Algorithm
intervals
Results
14.6s38981×body80nan
5.5s12876×body80valid