Details

Time bar (total: 22.5s)

sample274.0ms

Algorithm
intervals
Results
145.0ms1124×body80nan
65.0ms408×body80valid

simplify187.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 24.0b

Counts
2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* (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))))
10.8b
(pow (/ d h) (/ 1.0 2.0))
11.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.2b
(pow (/ d l) (/ 1.0 2.0))

rewrite49.0ms

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:
14.0ms
(* (* (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 h) (/ 1.0 2.0))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
633.0ms
(* (* (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))))
60.0ms
(pow (/ d h) (/ 1.0 2.0))
768.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
66.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012282042
150011847

prune663.0ms

Filtered
188 candidates to 109 candidates (58.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New17018188
Fresh000
Picked101
Done000
Total17118189

Merged error: 10.0b

Counts
189 → 18

localize42.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
6.0b
(* (* (* (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))))
11.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.2b
(pow (/ d l) (/ 1.0 2.0))

rewrite77.0ms

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:
6.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(* (* (* (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))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (* M D) (* 2.0 d))
638.0ms
(* (* (* (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))))
743.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
69.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify73.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
016425552
150025211

prune681.0ms

Filtered
272 candidates to 88 candidates (32.4%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New2657272
Fresh21517
Picked101
Done000
Total26822290

Merged error: 9.3b

Counts
290 → 22

localize54.0ms

Local error

Found 4 expressions with local error:

1.8b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
3.8b
(/ (* M D) (* 2.0 d))
6.0b
(* (* (* (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)) (* (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)) (/ h l))))
11.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
5947×add-exp-log
4317×prod-exp
1997×pow-exp
1387×div-exp
643×pow-to-exp
55×add-cbrt-cube
27×cbrt-unprod
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv
5×unpow-prod-down
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 → 983
Calls
4 calls:
19.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
75.0ms
(* (* (* (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)) (* (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)) (/ h l))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
127.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
28.0ms
(/ (* M D) (* 2.0 d))
701.0ms
(* (* (* (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)) (* (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)) (/ h l))))
757.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify333.0ms

Algorithm
egg-herbie
Counts
995 → 995
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0408038233
1500238031

prune867.0ms

Filtered
995 candidates to 89 candidates (8.9%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New9914995
Fresh21921
Picked101
Done000
Total994231017

Merged error: 7.6b

Counts
1017 → 23

localize56.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
6.0b
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
6.9b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
7.1b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
5908×add-exp-log
4305×prod-exp
1987×pow-exp
1368×div-exp
641×pow-to-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 → 950
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
75.0ms
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 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)
11.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

series2.4s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
639.0ms
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
945.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
767.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify336.0ms

Algorithm
egg-herbie
Counts
962 → 962
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0387637890
1500137685

prune602.0ms

Filtered
962 candidates to 69 candidates (7.2%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New9602962
Fresh12122
Picked101
Done000
Total96223985

Merged error: 7.6b

Counts
985 → 23

regimes1.2s

Accuracy

41.9% (4.2b remaining)

Error of 14.3b against oracle of 10.0b and baseline of 17.3b

bsearch633.0ms

Steps
ItersRangePoint
7
1.4604126510842042e-86
3.3061259117174557e-84
3.243471014017301e-84
9
-8.898150898178952e-79
-5.067645266206579e-84
-1.778789773596539e-79

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067169
167169

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.8s38051×body80nan
2.1s12817×body80valid