Details

Time bar (total: 4.3s)

sample73.0ms

Algorithm
intervals
Results
26.0ms53×body10240exit
16.0ms328×body80nan
15.0ms255×body80valid
1.0ms1×body1280valid

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.2b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite13.0ms

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:
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
6.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(sqrt (atan2 b b))

series89.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
60.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify74.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0255514
1714433
22703425
35001408

prune160.0ms

Filtered
72 candidates to 43 candidates (59.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))
0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.2b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
11×unpow-prod-up
9×prod-diff
7×pow1
6×unpow-prod-down sqrt-prod
5×add-exp-log pow-unpow log1p-expm1-u
4×expm1-log1p-u add-cbrt-cube add-log-exp
3×pow-pow
2×sqrt-pow1 pow1/2
1×pow-to-exp sub-neg rem-sqrt-square expm1-log1p pow-exp sqrt-pow2 distribute-lft-out-- expm1-udef pow-sub difference-of-squares sqr-pow
Counts
4 → 74
Calls
4 calls:
0.0ms
(expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
6.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(sqrt (atan2 b b))

series184.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
56.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
14.0ms
(sqrt (atan2 b b))

simplify100.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0296636
1869542
23455526
35001509

prune226.0ms

Filtered
86 candidates to 53 candidates (61.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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
(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
40×cbrt-prod
29×sqrt-prod
19×add-cube-cbrt *-un-lft-identity
14×pow1
11×swap-sqr
9×associate-*r* associate-*l* unswap-sqr
6×add-exp-log pow1/3
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 103
Calls
4 calls:
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
10.0ms
(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

series143.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
16.0ms
(sqrt (atan2 b b))
107.0ms
(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

simplify117.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 4 (110.0ms)

IterNodesCost
0103745
1354703
21192651
33474614
45001598

prune323.0ms

Filtered
115 candidates to 67 candidates (58.3%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
15.0ms
(sin (* (pow (* (pow (sqrt (cbrt (sqrt (atan2 b b)))) 3) (sqrt (cbrt (sqrt (atan2 b b))))) (- b a)) (pow (cbrt (sqrt (atan2 b b))) (- b a))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series178.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(sin (* (pow (* (pow (sqrt (cbrt (sqrt (atan2 b b)))) 3) (sqrt (cbrt (sqrt (atan2 b b))))) (- b a)) (pow (cbrt (sqrt (atan2 b b))) (- b a))))
13.0ms
(sqrt (atan2 b b))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify53.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0138447
1373396
21446383
35002382

prune272.0ms

Filtered
66 candidates to 50 candidates (75.8%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

regimes34.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01821
11821

end0.0ms

sample2.1s

Algorithm
intervals
Results
790.0ms1769×body10240exit
476.0ms7996×body80valid
472.0ms9746×body80nan
1.0ms1×body1280valid
0.0ms1×body640valid
0.0ms1×body320valid
0.0ms1×body160valid