Details

Time bar (total: 4.5s)

sample68.0ms

Algorithm
intervals
Results
21.0ms51×body10240exit
14.0ms255×body80valid
14.0ms306×body80nan
1.0ms1×body1280valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43215
516275
650015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (sqrt (atan2 b b)) (- b a))
0.2b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite27.0ms

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:
11.0ms
(pow (sqrt (atan2 b b)) (- b a))
12.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms
(sqrt (atan2 b b))

series80.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(pow (sqrt (atan2 b b)) (- b a))
53.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify77.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0255514
1714433
22703425
35001408

prune143.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.2b
(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))

rewrite43.0ms

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:
9.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
28.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series131.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
79.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
9.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify119.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (111.0ms)

IterNodesCost
0308751
1889651
24114639
35002636

prune250.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))))
0.3b
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
42×unpow-prod-down
29×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
24×cube-prod sqrt-prod
22×unpow-prod-up
18×prod-diff
6×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqr-pow
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×cube-div cube-mult cbrt-div pow1/3 unpow3 rem-cbrt-cube pow-sub
Counts
4 → 105
Calls
4 calls:
39.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))))
14.0ms
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series128.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))))
26.0ms
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify46.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04991200
116281037
250011031

prune280.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
29×sqrt-prod
27×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
18×unpow-prod-down
13×pow-unpow
12×pow1
11×unpow-prod-up
10×pow-pow sqrt-pow1
9×prod-diff
6×add-exp-log pow1/2
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-to-exp rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- difference-of-squares sqr-pow
1×sub-neg pow-sub
Counts
4 → 109
Calls
4 calls:
9.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
8.0ms
(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series249.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
203.0ms
(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify45.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0449993
11491883
25002842

prune350.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes41.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01314
11314

end0.0ms

sample2.2s

Algorithm
intervals
Results
804.0ms1896×body10240exit
465.0ms7993×body80valid
458.0ms9745×body80nan
2.0ms1×body5120valid
1.0ms2×body1280valid
1.0ms1×body2560valid
0.0ms2×body320valid
0.0ms1×body160valid