Details

Time bar (total: 21.4s)

sample249.0ms

Algorithm
intervals
Results
127.0ms1253×body80nan
57.0ms429×body80valid

simplify197.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize29.0ms

Local error

Found 4 expressions with local error:

8.0b
(* (* (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))))
10.4b
(pow (/ d l) (/ 1.0 2.0))
12.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
14.4b
(pow (/ d h) (/ 1.0 2.0))

rewrite75.0ms

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:
32.0ms
(* (* (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))))
4.0ms
(pow (/ d l) (/ 1.0 2.0))
25.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
649.0ms
(* (* (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))))
70.0ms
(pow (/ d l) (/ 1.0 2.0))
753.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
67.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012282042
150011847

prune714.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.8b

localize42.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
8.0b
(* (* (* (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))))
10.4b
(pow (/ d l) (/ 1.0 2.0))
12.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite252.0ms

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×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:
4.0ms
(/ (* M D) (* 2.0 d))
196.0ms
(* (* (* (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))))
4.0ms
(pow (/ d l) (/ 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:
33.0ms
(/ (* M D) (* 2.0 d))
635.0ms
(* (* (* (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))))
68.0ms
(pow (/ d l) (/ 1.0 2.0))
750.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify78.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
016425552
150025211

prune716.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.3b

localize52.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
7.5b
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
8.0b
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
10.4b
(pow (/ d l) (/ 1.0 2.0))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
978×add-exp-log
593×prod-exp
277×div-exp
236×pow-exp
82×pow-to-exp
71×add-cbrt-cube
41×add-sqr-sqrt
40×times-frac
38×cbrt-unprod
33×add-cube-cbrt *-un-lft-identity
27×cbrt-undiv
25×associate-*r*
13×unpow-prod-down pow-unpow
10×cbrt-prod
9×pow1
6×associate-*l*
5×div-inv
4×add-log-exp
3×associate-*r/ unswap-sqr
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg associate-*l/ clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 316
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
39.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
197.0ms
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
4.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
771.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
663.0ms
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
81.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify108.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
020917601
150017181

prune1.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.8b

localize59.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
4.6b
(/ (* M D) (* 2.0 d))
7.5b
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
8.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))

rewrite518.0ms

Algorithm
rewrite-expression-head
Rules
5855×add-exp-log
4246×prod-exp
2032×pow-exp
1549×div-exp
650×pow-to-exp
232×1-exp
95×add-cbrt-cube
52×cbrt-unprod
35×cbrt-undiv
27×add-sqr-sqrt
25×associate-*r*
23×times-frac
19×add-cube-cbrt *-un-lft-identity
11×pow1
10×cbrt-prod
6×associate-*l*
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ unswap-sqr
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in associate-*l/ clear-num associate-/r* *-commutative associate-/l*
1×frac-times flip3-- flip-- associate-/l/
Counts
4 → 1056
Calls
4 calls:
10.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
4.0ms
(/ (* M D) (* 2.0 d))
38.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
294.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
581.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
27.0ms
(/ (* M D) (* 2.0 d))
789.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
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 (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))

simplify613.0ms

Algorithm
egg-herbie
Counts
1068 → 1068
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0444939844
1500239446

prune913.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.5b

regimes1.2s

Accuracy

18% (3.9b remaining)

Error of 15.2b against oracle of 11.3b and baseline of 16.1b

bsearch5.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
090147
190147

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.8s38801×body80nan
1.7s12817×body80valid