Details

Time bar (total: 5.3s)

sample363.0ms

Algorithm
intervals
Results
57.0ms50×body5120exit
21.0ms349×body80nan
19.0ms255×body80valid
0.0ms1×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43215
516275
650015

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: 0.1b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.1b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
11×unpow-prod-up
9×prod-diff
6×pow1 unpow-prod-down sqrt-prod
5×pow-unpow
4×add-exp-log
3×expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2
1×pow-to-exp sub-neg rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
3 → 63
Calls
3 calls:
6.0ms
(pow (sqrt (atan2 b b)) (- b a))
5.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
16.0ms
(sqrt (atan2 b b))

series104.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(pow (sqrt (atan2 b b)) (- b a))
60.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms
(sqrt (atan2 b b))

simplify71.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0255515
1727433
22663425
35001408

prune125.0ms

Filtered
72 candidates to 43 candidates (59.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New70272
Fresh000
Picked101
Done000
Total71273

Merged error: 0.1b

Counts
73 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
15×sqrt-prod
11×unpow-prod-up
9×pow1 unpow-prod-down prod-diff
6×sqrt-pow1
5×add-exp-log pow-unpow pow-pow
4×expm1-log1p-u pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square
1×pow-to-exp sub-neg pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 83
Calls
4 calls:
7.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
3.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series133.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
87.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify122.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (114.0ms)

IterNodesCost
0308751
1889651
24114639
35002636

prune212.0ms

Filtered
95 candidates to 60 candidates (63.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New93295
Fresh011
Picked101
Done000
Total94397

Merged error: 0.1b

Counts
97 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series43.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(sqrt (atan2 b b))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify99.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 7 (29.0ms)

IterNodesCost
024212
127208
230208
335208
454208
5108208
6535208
71774204
85001204

prune210.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh022
Picked011
Done000
Total72375

Merged error: 0.1b

Counts
75 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow (atan2 b b) (/ (- b a) 2))
0.1b
(sin (pow (atan2 b b) (/ (- b a) 2)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
19×pow-unpow
18×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
3×pow1 add-exp-log unpow-prod-down distribute-lft-out-- difference-of-squares
2×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
1×pow-to-exp pow-pow div-sub pow-exp div-inv pow-sub sqr-pow
Counts
2 → 45
Calls
2 calls:
6.0ms
(pow (atan2 b b) (/ (- b a) 2))
3.0ms
(sin (pow (atan2 b b) (/ (- b a) 2)))

series82.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(pow (atan2 b b) (/ (- b a) 2))
62.0ms
(sin (pow (atan2 b b) (/ (- b a) 2)))

simplify76.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0238341
1772323
23169307
35001304

prune100.0ms

Filtered
51 candidates to 38 candidates (74.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New51051
Fresh011
Picked011
Done011
Total51354

Merged error: 0.1b

Counts
54 → 3

regimes39.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01427
11427

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.8s1815×body5120exit
625.0ms7989×body80valid
568.0ms9961×body80nan
3.0ms1×body5120valid
3.0ms2×body2560valid
2.0ms2×body1280valid
1.0ms6×body160valid