Details

Time bar (total: 4.7s)

sample319.0ms

Algorithm
intervals
Results
21.0ms48×body10240exit
16.0ms256×body80valid
15.0ms320×body80nan

simplify56.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b
(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:
7.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
3.0ms
(sqrt (atan2 b b))

series103.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms
(pow (sqrt (atan2 b b)) (- b a))
18.0ms
(sqrt (atan2 b b))

simplify75.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0255514
1714433
22702425
35002408

prune152.0ms

Filtered
72 candidates to 43 candidates (59.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b
(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
32×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
24×sqrt-prod
22×unpow-prod-up
18×unpow-prod-down prod-diff
12×pow1
10×pow-unpow pow-pow sqrt-pow1
6×add-exp-log pow1/2
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-to-exp sub-neg rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 118
Calls
4 calls:
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series75.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
29.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify82.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
02641026
1731882
22885870
35002838

prune304.0ms

Filtered
130 candidates to 72 candidates (55.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
2.7b
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×*-un-lft-identity
26×add-cube-cbrt
24×log-prod sqrt-prod
22×unpow-prod-up
18×unpow-prod-down prod-diff
9×pow1
7×add-exp-log
6×sqrt-pow1
5×pow-unpow pow-pow
4×expm1-log1p-u pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-log-exp
2×pow-to-exp sub-neg rem-sqrt-square pow-exp pow-sub sqr-pow
1×log-div log-pow sqrt-pow2 distribute-lft-out-- difference-of-squares
Counts
4 → 112
Calls
4 calls:
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
5.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series132.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
82.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify116.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
03451080
1985903
23991894
35001893

prune340.0ms

Filtered
124 candidates to 71 candidates (57.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

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))
2.7b
(log (* (pow (* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b))))) (- b a)) (pow (cbrt (sqrt (sqrt (atan2 b b)))) (- b a))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
15×prod-exp
13×rem-log-exp
10×add-sqr-sqrt pow-exp
9×sqrt-prod
8×pow1
7×pow-to-exp add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u pow-sub add-log-exp
3×rem-sqrt-square log-div sqrt-pow1 pow1/2 log-pow
1×frac-times unpow-prod-down log-prod associate-*r/ pow3 pow-prod-down associate-*l/
Counts
4 → 74
Calls
4 calls:
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
14.0ms
(log (* (pow (* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b))))) (- b a)) (pow (cbrt (sqrt (sqrt (atan2 b b)))) (- b a))))

series182.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
14.0ms
(sqrt (atan2 b b))
147.0ms
(log (* (pow (* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b))))) (- b a)) (pow (cbrt (sqrt (sqrt (atan2 b b)))) (- b a))))

simplify49.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0155582
1413536
21562457
35001444

prune355.0ms

Filtered
86 candidates to 61 candidates (70.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes37.0ms

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
01214
11214

end0.0ms

sample2.2s

Algorithm
intervals
Results
846.0ms1918×body10240exit
473.0ms9919×body80nan
457.0ms7987×body80valid
5.0ms4×body2560valid
2.0ms4×body640valid
1.0ms1×body1280valid
1.0ms4×body160valid