Details

Time bar (total: 2.5m)

sample785.0ms

Algorithm
intervals
Results
488.0ms1183×body80nan
216.0ms421×body80valid

simplify347.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
347.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize45.0ms

Local error

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)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity add-cube-cbrt
11×pow1
add-cbrt-cube add-exp-log
sqrt-div
expm1-log1p-u rem-sqrt-square associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
associate-*l* pow-prod-down prod-exp cbrt-unprod
sqrt-pow1 pow1/2 div-inv
frac-times associate-*r* associate-*l/ *-commutative fma-udef
Counts
4 → 91
Calls
4 calls:
Slowest
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)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
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))

simplify7.1s

Counts
124 → 103
Calls
124 calls:
Slowest
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)))))

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.1b

localize97.0ms

Local error

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))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
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
associate-/r* prod-exp cbrt-unprod
pow-prod-down associate-*r/ div-inv
cbrt-undiv sqrt-div div-exp
expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
associate-*l* associate-/l*
rem-sqrt-square
frac-times clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l/ associate-/r/ *-commutative fma-udef
Counts
4 → 117
Calls
4 calls:
Slowest
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)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
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))

simplify15.3s

Counts
161 → 129
Calls
161 calls:
Slowest
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)))))))

prune3.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 12.5b

localize121.0ms

Local error

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))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
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
associate-*r/
associate-/l*
expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
associate-*l*
clear-num frac-2neg associate-/r/
frac-times associate-*r* associate-*l/ *-commutative fma-udef
Counts
4 → 146
Calls
4 calls:
Slowest
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)

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
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))

simplify25.2s

Counts
201 → 158
Calls
201 calls:
Slowest
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)))))))

prune4.0s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 10.8b

localize104.0ms

Local error

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)

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
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
frac-times associate-*l/
sqrt-div
expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
rem-sqrt-square associate-/r* div-inv
*-commutative unswap-sqr
clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l*
Counts
4 → 171
Calls
4 calls:
Slowest
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))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
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)

simplify49.2s

Counts
209 → 183
Calls
209 calls:
Slowest
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)))

prune3.9s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 8.2b

regimes2.8s

Accuracy

30.4% (4.3b remaining)

Error of 11.6b against oracle of 7.2b and baseline of 13.4b

bsearch1.3s

end0.0ms

sample25.5s

Algorithm
intervals
Results
17.3s38146×body80nan
5.7s12695×body80valid