Details

Time bar (total: 21.8s)

sample244.0ms

Algorithm
intervals
Results
123.0ms1253×body80nan
56.0ms429×body80valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
272017
3500117

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize32.0ms

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))

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

series1.5s

Counts
4 → 12
Calls
4 calls:
644.0ms
(* (* (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))))
66.0ms
(pow (/ d l) (/ 1.0 2.0))
747.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
70.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012872382
150012125

prune749.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.8b

localize46.0ms

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×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:
4.0ms
(/ (* M D) (* 2.0 d))
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)) (/ h l))))
4.0ms
(pow (/ d l) (/ 1.0 2.0))
22.0ms
(* (* (/ 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))
651.0ms
(* (* (* (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))))
62.0ms
(pow (/ d l) (/ 1.0 2.0))
763.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify91.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
017106060
150015717

prune875.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.3b

localize51.0ms

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))

rewrite269.0ms

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
43×add-sqr-sqrt
40×times-frac
38×cbrt-unprod
35×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* prod-diff
5×distribute-rgt-in distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ unswap-sqr
2×sub-neg 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 → 330
Calls
4 calls:
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)))
193.0ms
(* (* (* (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)))))
5.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
820.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
676.0ms
(* (* (* (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)))))
69.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify114.0ms

Algorithm
egg-herbie
Counts
342 → 342
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
021588219
150017731

prune1.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.8b

localize62.0ms

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)))))

rewrite525.0ms

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
29×add-sqr-sqrt
25×associate-*r*
23×times-frac
21×add-cube-cbrt *-un-lft-identity
11×pow1
10×cbrt-prod
6×associate-*l* 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/ unswap-sqr
2×sub-neg frac-2neg associate-*l/ clear-num associate-/r* *-commutative associate-/l*
1×frac-times flip3-- flip-- associate-/l/
Counts
4 → 1070
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))
40.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
302.0ms
(* (* (* (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)))))

series2.7s

Counts
4 → 12
Calls
4 calls:
537.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
29.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
1.1s
(* (* (* (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)))))

simplify385.0ms

Algorithm
egg-herbie
Counts
1082 → 1082
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0453540588
1500239373

prune1.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.5b

regimes1.3s

Accuracy

18.1% (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

sample7.1s

Algorithm
intervals
Results
3.7s38801×body80nan
1.7s12817×body80valid