Details

Time bar (total: 22.4s)

sample300.0ms

Algorithm
intervals
Results
165.0ms1315×body80nan
66.0ms413×body80valid

simplify192.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

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: 22.9b

Counts
2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

5.3b
(/ (* M D) (* 2.0 d))
9.1b
(pow (/ d h) (/ 1.0 2.0))
10.4b
(pow (/ d l) (/ 1.0 2.0))
14.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
26×unpow-prod-down pow-unpow
24×pow-exp
14×cbrt-unprod
13×associate-*r*
9×cbrt-undiv
8×pow1
6×pow-to-exp div-inv
4×add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 159
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
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))

series906.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (* M D) (* 2.0 d))
60.0ms
(pow (/ d h) (/ 1.0 2.0))
66.0ms
(pow (/ d l) (/ 1.0 2.0))
746.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify106.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010711320
147091160
250011160

prune656.0ms

Filtered
171 candidates to 104 candidates (60.8%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New15021171
Fresh000
Picked101
Done000
Total15121172

Merged error: 11.0b

Counts
172 → 21

localize47.0ms

Local error

Found 4 expressions with local error:

3.8b
(* (* (* (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))))
5.3b
(/ (* M D) (* 2.0 d))
10.4b
(pow (/ d l) (/ 1.0 2.0))
14.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite81.0ms

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:
31.0ms
(* (* (* (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))))
6.0ms
(/ (* M D) (* 2.0 d))
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))

series1.5s

Counts
4 → 12
Calls
4 calls:
647.0ms
(* (* (* (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))))
34.0ms
(/ (* M D) (* 2.0 d))
60.0ms
(pow (/ d l) (/ 1.0 2.0))
746.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify83.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
016425552
150025211

prune714.0ms

Filtered
272 candidates to 90 candidates (33.1%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New26111272
Fresh81220
Picked101
Done000
Total27023293

Merged error: 9.7b

Counts
293 → 23

localize54.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
3.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
5.3b
(/ (* M D) (* 2.0 d))
14.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
32×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
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1229
Calls
4 calls:
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
87.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
6.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
173.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.2s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
27.0ms
(/ (* M D) (* 2.0 d))
748.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify377.0ms

Algorithm
egg-herbie
Counts
1241 → 1241
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500145012

prune1.2s

Filtered
1241 candidates to 131 candidates (10.6%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New123651241
Fresh12122
Picked101
Done000
Total1238261264

Merged error: 7.7b

Counts
1264 → 26

localize60.0ms

Local error

Found 4 expressions with local error:

3.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
5.3b
(/ (* M D) (* 2.0 d))
5.9b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.7b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
6936×add-exp-log
5237×prod-exp
2607×pow-exp
1610×div-exp
787×pow-to-exp
232×rec-exp 1-exp
60×add-cbrt-cube
29×cbrt-unprod
11×pow1
10×cbrt-undiv
8×add-sqr-sqrt *-un-lft-identity associate-*r*
6×add-cube-cbrt
4×pow-prod-down add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac associate-*r/ associate-*l* clear-num associate-/r* *-commutative div-inv associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1182
Calls
4 calls:
87.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
6.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
8.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

series2.4s

Counts
4 → 12
Calls
4 calls:
967.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
28.0ms
(/ (* M D) (* 2.0 d))
714.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
704.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

simplify376.0ms

Algorithm
egg-herbie
Counts
1194 → 1194
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0479343179
1500242997

prune595.0ms

Filtered
1194 candidates to 72 candidates (6.0%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New119131194
Fresh22325
Picked101
Done000
Total1194261220

Merged error: 7.6b

Counts
1220 → 26

regimes1.1s

Accuracy

7.4% (5.7b remaining)

Error of 15.8b against oracle of 10.1b and baseline of 16.2b

bsearch301.0ms

Steps
ItersRangePoint
10
5.73742411594878e-07
219918812.92704484
0.007223838275094958

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06579
16579

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.7s38596×body80nan
2.0s12816×body80valid