Details

Time bar (total: 22.7s)

sample249.0ms

Algorithm
intervals
Results
126.0ms1225×body80nan
57.0ms421×body80valid

simplify35.0ms

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: 26.6b

localize30.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (* (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))))
9.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.8b
(pow (/ d l) (/ 1.0 2.0))
13.1b
(pow (/ d h) (/ 1.0 2.0))

rewrite77.0ms

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:
37.0ms
(* (* (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))))
23.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d l) (/ 1.0 2.0))
5.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
642.0ms
(* (* (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))))
759.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
62.0ms
(pow (/ d l) (/ 1.0 2.0))
68.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012872382
150012125

prune751.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.0b

localize44.0ms

Local error

Found 4 expressions with local error:

3.6b
(pow (/ (cbrt d) h) (/ 1.0 2.0))
7.0b
(* (* (* (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))))
9.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
665×add-exp-log
451×prod-exp
218×pow-exp
168×div-exp
79×pow-to-exp
54×times-frac
48×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
35×unpow-prod-down
34×add-cbrt-cube
32×1-exp
26×pow-unpow
16×associate-*r* cbrt-unprod
10×pow1
9×cbrt-prod
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 → 300
Calls
4 calls:
6.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
143.0ms
(* (* (* (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))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
164.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
991.0ms
(* (* (* (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))))
754.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
71.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify84.0ms

Algorithm
egg-herbie
Counts
312 → 312
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
018685708
150015254

prune973.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.9b

localize57.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* M D) (* 2.0 d))
3.6b
(pow (/ (cbrt d) h) (/ 1.0 2.0))
7.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
9.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
6373×add-exp-log
4949×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
528×1-exp
232×rec-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:
4.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
268.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
23.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
179.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
734.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
763.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify345.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500139780

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.9b

localize65.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* M D) (* 2.0 d))
3.6b
(pow (/ (cbrt d) h) (/ 1.0 2.0))
6.0b
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
7.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))

rewrite611.0ms

Algorithm
rewrite-expression-head
Rules
6613×add-exp-log
5113×prod-exp
2634×pow-exp
1674×div-exp
793×pow-to-exp
528×1-exp
232×rec-exp
84×add-cbrt-cube
55×cbrt-unprod
46×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×associate-*r*
22×unpow-prod-down
18×cbrt-prod
17×cbrt-undiv
15×pow1
13×pow-unpow
6×prod-diff pow-prod-down
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* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1293
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
127.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
271.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))

series2.0s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
172.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
982.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
797.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))

simplify391.0ms

Algorithm
egg-herbie
Counts
1305 → 1305
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500146704

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.4b

regimes1.0s

Accuracy

0% (6.0b remaining)

Error of 15.1b against oracle of 9.1b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05146
15146

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.8s37995×body80nan
1.7s12847×body80valid