Details

Time bar (total: 23.1s)

sample295.0ms

Algorithm
intervals
Results
162.0ms1315×body80nan
65.0ms413×body80valid

simplify32.0ms

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: 22.9b

Counts
2 → 1

localize29.0ms

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))

rewrite36.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 167
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
5.0ms
(pow (/ d l) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series887.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
66.0ms
(pow (/ d h) (/ 1.0 2.0))
65.0ms
(pow (/ d l) (/ 1.0 2.0))
728.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify104.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010791362
147211202
250011202

prune918.0ms

Filtered
179 candidates to 112 candidates (62.6%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New15821179
Fresh000
Picked101
Done000
Total15921180

Merged error: 11.0b

Counts
180 → 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))

rewrite78.0ms

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:
29.0ms
(* (* (* (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))

series1.4s

Counts
4 → 12
Calls
4 calls:
624.0ms
(* (* (* (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))))
33.0ms
(/ (* M D) (* 2.0 d))
60.0ms
(pow (/ d l) (/ 1.0 2.0))
709.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify86.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
017106060
150015717

prune831.0ms

Filtered
286 candidates to 106 candidates (37.1%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New27511286
Fresh81220
Picked101
Done000
Total28423307

Merged error: 9.7b

Counts
307 → 23

localize58.0ms

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))

rewrite309.0ms

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
34×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
6×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/ 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 → 1243
Calls
4 calls:
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
77.0ms
(* (* (* (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))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
185.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
984.0ms
(* (* (* (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))))
27.0ms
(/ (* M D) (* 2.0 d))
739.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify384.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500145180

prune1.4s

Filtered
1255 candidates to 145 candidates (11.6%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New125051255
Fresh12122
Picked101
Done000
Total1252261278

Merged error: 7.7b

Counts
1278 → 26

localize61.0ms

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)

rewrite317.0ms

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
30×prod-diff
29×cbrt-unprod
24×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
17×distribute-rgt-in distribute-lft-in
11×pow1
10×cbrt-undiv
8×times-frac associate-*r* div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num associate-/r* *-commutative associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1220
Calls
4 calls:
81.0ms
(* (* (* (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))))
7.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(/ (* (* 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)

series2.5s

Counts
4 → 12
Calls
4 calls:
973.0ms
(* (* (* (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))))
27.0ms
(/ (* M D) (* 2.0 d))
725.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
744.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

simplify385.0ms

Algorithm
egg-herbie
Counts
1232 → 1232
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500146277

prune1.1s

Filtered
1232 candidates to 111 candidates (9.0%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New122931232
Fresh22325
Picked101
Done000
Total1232261258

Merged error: 7.6b

Counts
1258 → 26

regimes1.1s

Accuracy

7.4% (5.7b remaining)

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

bsearch316.0ms

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