Details

Time bar (total: 19.5s)

sample316.0ms

Algorithm
intervals
Results
176.0ms1530×body80nan
65.0ms434×body80valid

simplify188.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize212.0ms

Local error

Found 4 expressions with local error:

7.3b
(* (* (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))))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.7b
(pow (/ d l) (/ 1.0 2.0))
13.0b
(pow (/ d h) (/ 1.0 2.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 176
Calls
4 calls:
14.0ms
(* (* (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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
6.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
611.0ms
(* (* (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))))
726.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))
65.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
012282042
150011847

prune722.0ms

Filtered
188 candidates to 109 candidates (58.0%)
Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.1b

localize39.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
7.3b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.7b
(pow (/ d l) (/ 1.0 2.0))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
674×add-exp-log
455×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
32×1-exp
28×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in 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 → 260
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
23.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (* M D) (* 2.0 d))
966.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
720.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
65.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
016674960
150014530

prune673.0ms

Filtered
272 candidates to 89 candidates (32.7%)
Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.6b

localize47.0ms

Local error

Found 4 expressions with local error:

11.7b
(pow (/ d l) (/ 1.0 2.0))
13.0b
(cbrt (/ h l))
13.0b
(cbrt (/ h l))
13.0b
(cbrt (/ h l))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
39×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×unpow-prod-down pow-unpow
7×add-exp-log
5×pow1 div-inv
4×add-cbrt-cube add-log-exp
3×cbrt-div pow1/3
2×pow-exp
1×pow-to-exp pow-pow div-exp sqr-pow
Counts
4 → 104
Calls
4 calls:
5.0ms
(pow (/ d l) (/ 1.0 2.0))
2.0ms
(cbrt (/ h l))
2.0ms
(cbrt (/ h l))
2.0ms
(cbrt (/ h l))

series248.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ d l) (/ 1.0 2.0))
62.0ms
(cbrt (/ h l))
63.0ms
(cbrt (/ h l))
58.0ms
(cbrt (/ h l))

simplify75.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0357682
11011650
23797644
35002620

prune819.0ms

Filtered
116 candidates to 92 candidates (79.3%)
Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 10.6b

localize40.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ M (/ (* 2.0 d) D))
7.3b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ M (/ (* 2.0 d) D)) 2.0)) (/ h l))))
10.9b
(* (* (/ 1.0 2.0) (pow (/ M (/ (* 2.0 d) D)) 2.0)) (/ h l))
11.7b
(pow (/ d l) (/ 1.0 2.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
647×add-exp-log
432×prod-exp
212×pow-exp
172×div-exp
78×pow-to-exp
60×times-frac
43×add-cbrt-cube
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×1-exp
17×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
10×cbrt-undiv
9×pow1
8×div-inv
7×associate-/r*
4×add-log-exp
3×associate-*r/ associate-*l/ associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r/ flip-- sqr-pow
Counts
4 → 283
Calls
4 calls:
10.0ms
(/ M (/ (* 2.0 d) D))
24.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ M (/ (* 2.0 d) D)) 2.0)) (/ h l))))
15.0ms
(* (* (/ 1.0 2.0) (pow (/ M (/ (* 2.0 d) D)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ M (/ (* 2.0 d) D))
936.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ M (/ (* 2.0 d) D)) 2.0)) (/ h l))))
738.0ms
(* (* (/ 1.0 2.0) (pow (/ M (/ (* 2.0 d) D)) 2.0)) (/ h l))
66.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify76.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
017485112
150024688

prune709.0ms

Filtered
295 candidates to 113 candidates (38.3%)
Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 10.6b

regimes1.2s

Accuracy

-2% (7.7b remaining)

Error of 18.5b against oracle of 10.8b and baseline of 18.4b

bsearch584.0ms

Steps
ItersRangePoint
10
3.6042865255625235e+246
2.871632757105746e+258
8.572141158221411e+252
10
1.3153541594715413e+131
3.191987100616305e+144
5.930206285185348e+142

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06446
16446

end0.0ms

sample8.1s

Algorithm
intervals
Results
4.4s38965×body80nan
1.9s12792×body80valid