Details

Time bar (total: 21.4s)

sample264.0ms

Algorithm
intervals
Results
137.0ms1242×body80nan
61.0ms413×body80valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
272017
3500117

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.1b

Counts
2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* (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))))
9.0b
(pow (/ d l) (/ 1.0 2.0))
11.4b
(pow (/ d h) (/ 1.0 2.0))
11.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite53.0ms

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:
18.0ms
(* (* (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))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
643.0ms
(* (* (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))
60.0ms
(pow (/ d h) (/ 1.0 2.0))
739.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify51.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012872382
150022125

prune769.0ms

Filtered
202 candidates to 119 candidates (58.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New18319202
Fresh000
Picked101
Done000
Total18419203

Merged error: 11.4b

Counts
203 → 19

localize46.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* M D) (* 2.0 d))
6.1b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
9.0b
(pow (/ d l) (/ 1.0 2.0))
11.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
818×add-exp-log
567×prod-exp
280×pow-exp
187×div-exp
94×pow-to-exp
46×add-cbrt-cube
32×rec-exp 1-exp
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 → 306
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
884.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))
744.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify82.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
018766250
150025934

prune817.0ms

Filtered
318 candidates to 105 candidates (33.0%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New30711318
Fresh31518
Picked101
Done000
Total31126337

Merged error: 10.7b

Counts
337 → 26

localize52.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
5.8b
(/ (* M D) (* 2.0 d))
6.1b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
9.0b
(pow (/ d l) (/ 1.0 2.0))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
1118×add-exp-log
738×prod-exp
310×pow-exp
277×div-exp
100×pow-to-exp
70×add-cbrt-cube
47×cbrt-unprod
32×rec-exp 1-exp
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×cbrt-undiv
20×times-frac
13×unpow-prod-down pow-unpow
9×pow1
8×associate-*r*
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 → 352
Calls
4 calls:
18.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
6.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
582.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
29.0ms
(/ (* M D) (* 2.0 d))
872.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
70.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify115.0ms

Algorithm
egg-herbie
Counts
364 → 364
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
021769545
150028878

prune964.0ms

Filtered
364 candidates to 104 candidates (28.6%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New3577364
Fresh61925
Picked101
Done000
Total36426390

Merged error: 10.2b

Counts
390 → 26

localize67.0ms

Local error

Found 4 expressions with local error:

2.7b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
5.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
5.8b
(/ (* M D) (* 2.0 d))
6.1b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt 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 l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

rewrite381.0ms

Algorithm
rewrite-expression-head
Rules
7275×add-exp-log
5420×prod-exp
2647×pow-exp
1719×div-exp
795×pow-to-exp
232×rec-exp 1-exp
79×add-cbrt-cube
54×cbrt-unprod
21×cbrt-undiv
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×pow-unpow
12×pow1 times-frac
8×associate-*r*
6×prod-diff
5×distribute-rgt-in unpow-prod-down 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 → 1275
Calls
4 calls:
12.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
19.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
6.0ms
(/ (* M D) (* 2.0 d))
86.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt 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 l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
120.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
583.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
28.0ms
(/ (* M D) (* 2.0 d))
904.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt 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 l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

simplify451.0ms

Algorithm
egg-herbie
Counts
1287 → 1287
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500157825

prune1.2s

Filtered
1287 candidates to 129 candidates (10.0%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New128341287
Fresh12425
Picked101
Done000
Total1285281313

Merged error: 9.8b

Counts
1313 → 28

regimes1.4s

Accuracy

0% (5.1b remaining)

Error of 15.4b against oracle of 10.3b and baseline of 15.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04847
14847

end0.0ms

sample7.8s

Algorithm
intervals
Results
4.1s38342×body80nan
1.9s12902×body80valid