Details

Time bar (total: 4.6s)

sample420.0ms

Algorithm
intervals
Results
56.0ms62×body10240exit
16.0ms332×body80nan
15.0ms254×body80valid
1.0ms1×body1280valid
0.0ms1×body640valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43215
516275
650015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.4b
(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:
8.0ms
(pow (sqrt (atan2 b b)) (- b a))
12.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms
(sqrt (atan2 b b))

series101.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(pow (sqrt (atan2 b b)) (- b a))
66.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms
(sqrt (atan2 b b))

simplify77.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0255514
1714433
22703425
35001408

prune151.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.5b
(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))

rewrite46.0ms

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:
10.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
31.0ms
(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))

series128.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
83.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify121.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (111.0ms)

IterNodesCost
0308751
1889651
24114639
35002636

prune257.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))
0.4b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×expm1-log1p expm1-udef
Counts
4 → 50
Calls
4 calls:
0.0ms
(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))
16.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series204.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))
131.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify41.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (36.0ms)

IterNodesCost
0114432
1271380
21026371
35001366

prune220.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))
0.4b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×expm1-log1p expm1-udef
Counts
4 → 50
Calls
4 calls:
0.0ms
(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))
16.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series202.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))
126.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
9.0ms
(sqrt (atan2 b b))
9.0ms
(sqrt (atan2 b b))

simplify40.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
0114432
1271380
21026371
35001366

prune238.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes44.0ms

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
01416
11416

end0.0ms

sample2.1s

Algorithm
intervals
Results
760.0ms1786×body10240exit
463.0ms7992×body80valid
445.0ms9625×body80nan
1.0ms3×body640valid
1.0ms1×body2560valid
1.0ms1×body1280valid
0.0ms2×body160valid
0.0ms1×body320valid