Details

Time bar (total: 3.6s)

sample70.0ms

Algorithm
intervals
Results
28.0ms72×body10240exit
14.0ms256×body80valid
12.0ms348×body80nan

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43215
516275
650015

prune2.0ms

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: 0.0b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

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:
9.0ms
(pow (sqrt (atan2 b b)) (- b a))
5.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(sqrt (atan2 b b))

series84.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
56.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify78.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0255514
1714433
22703425
35001408

prune147.0ms

Filtered
72 candidates to 43 candidates (59.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New69372
Fresh000
Picked101
Done000
Total70373

Merged error: 0b

Counts
73 → 3

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
1 → 9
Calls
1 calls:
6.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

series60.0ms

Counts
1 → 3
Calls
1 calls:
60.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify75.0ms

Algorithm
egg-herbie
Counts
12 → 12
Iterations

Useful iterations: 4 (30.0ms)

IterNodesCost
068101
116689
245782
3110581
4279879
5500179

prune35.0ms

Filtered
12 candidates to 10 candidates (83.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New11112
Fresh112
Picked011
Done000
Total12315

Merged error: 0b

Counts
15 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
0.0b
(log (exp (pow (sqrt (atan2 b b)) (- b a))))
0.0b
(exp (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
42×exp-prod
26×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
22×unpow-prod-up log-pow
18×prod-diff
12×unpow-prod-down
9×sqrt-prod
6×pow1 log-prod
5×add-log-exp
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×sin-sum
2×sub-neg sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp rem-exp-log
Counts
4 → 93
Calls
4 calls:
8.0ms
(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
7.0ms
(log (exp (pow (sqrt (atan2 b b)) (- b a))))
11.0ms
(exp (pow (sqrt (atan2 b b)) (- b a)))
2.0ms
(sqrt (atan2 b b))

series119.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
19.0ms
(log (exp (pow (sqrt (atan2 b b)) (- b a))))
30.0ms
(exp (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify61.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0292800
1679676
22202661
35001612

prune263.0ms

Filtered
105 candidates to 69 candidates (65.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1041105
Fresh101
Picked011
Done011
Total1053108

Merged error: 0b

Counts
108 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (pow (sqrt (atan2 b b)) (- b a)))
0.0b
(expm1 (log1p (exp (pow (sqrt (atan2 b b)) (- b a)))))
1.0b
(sqrt (atan2 b b))
42.7b
(log (expm1 (log1p (exp (pow (sqrt (atan2 b b)) (- b a))))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
21×exp-prod
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×unpow-prod-up
9×prod-diff
6×pow1 unpow-prod-down sqrt-prod
5×add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×log-prod
1×sub-neg rem-sqrt-square expm1-log1p sqrt-pow1 pow1/2 rem-log-exp log-pow rem-exp-log expm1-udef sqr-pow
Counts
4 → 71
Calls
4 calls:
6.0ms
(exp (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(expm1 (log1p (exp (pow (sqrt (atan2 b b)) (- b a)))))
2.0ms
(sqrt (atan2 b b))
1.0ms
(log (expm1 (log1p (exp (pow (sqrt (atan2 b b)) (- b a))))))

series174.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(exp (pow (sqrt (atan2 b b)) (- b a)))
58.0ms
(expm1 (log1p (exp (pow (sqrt (atan2 b b)) (- b a)))))
9.0ms
(sqrt (atan2 b b))
71.0ms
(log (expm1 (log1p (exp (pow (sqrt (atan2 b b)) (- b a))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0234558
1563463
21767450
35001429

prune232.0ms

Filtered
83 candidates to 55 candidates (66.3%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New83083
Fresh000
Picked011
Done022
Total83386

Merged error: 0b

Counts
86 → 3

regimes59.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0119

end0.0ms

sample1.9s

Algorithm
intervals
Results
762.0ms1803×body10240exit
444.0ms7988×body80valid
346.0ms9775×body80nan
2.0ms2×body2560valid
1.0ms2×body1280valid
1.0ms3×body640valid
1.0ms4×body160valid
0.0ms1×body320valid