Details

Time bar (total: 31.3s)

sample456.0ms

Algorithm
intervals
Results
269.0ms1245×body80nan
118.0ms406×body80valid

simplify32.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
272017
3500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize32.0ms

Local error

Found 4 expressions with local error:

5.0b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.2b
(pow (/ d l) (/ 1.0 2.0))
11.5b
(pow (/ d h) (/ 1.0 2.0))
13.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
40×pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×cbrt-undiv distribute-rgt-in distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 190
Calls
4 calls:
39.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms
(pow (/ d l) (/ 1.0 2.0))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
25.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
652.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
68.0ms
(pow (/ d l) (/ 1.0 2.0))
61.0ms
(pow (/ d h) (/ 1.0 2.0))
758.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify49.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012872382
150022125

prune813.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.8b

localize42.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
5.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.2b
(pow (/ d l) (/ 1.0 2.0))
13.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 274
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
214.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms
(pow (/ d l) (/ 1.0 2.0))
24.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
655.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
69.0ms
(pow (/ d l) (/ 1.0 2.0))
756.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify81.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
017106060
150015717

prune950.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 10.1b

localize55.0ms

Local error

Found 4 expressions with local error:

1.9b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.0b
(/ (* M D) (* 2.0 d))
5.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite782.0ms

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
34×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv cbrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1243
Calls
4 calls:
6.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
346.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
27.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
185.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
28.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
754.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify371.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500145180

prune1.6s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 9.0b

localize63.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
4.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
5.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
6.8b
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

rewrite719.0ms

Algorithm
rewrite-expression-head
Rules
7251×add-exp-log
5438×prod-exp
2642×pow-exp
1681×div-exp
794×pow-to-exp
232×rec-exp 1-exp
87×add-cbrt-cube
58×cbrt-unprod
26×associate-*r*
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×times-frac
17×cbrt-undiv
14×pow1
11×associate-*l*
9×cbrt-prod
6×unpow-prod-down prod-diff pow-prod-down
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/ *-commutative div-inv unswap-sqr
2×sub-neg sqr-pow
1×frac-times flip3-- frac-2neg clear-num associate-/r* flip-- associate-/l*
Counts
4 → 1283
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
19.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
347.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
135.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

series2.3s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
463.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
1.0s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
818.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

simplify414.0ms

Algorithm
egg-herbie
Counts
1295 → 1295
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500152101

prune1.4s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 7.9b

regimes1.8s

Accuracy

0% (5.0b remaining)

Error of 14.1b against oracle of 9.0b and baseline of 14.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05049
15049

end0.0ms

sample13.9s

Algorithm
intervals
Results
8.3s38476×body80nan
3.8s13071×body80valid