Details

Time bar (total: 5.2s)

sample113.0ms

Algorithm
intervals
Results
52.0ms50×body5120exit
23.0ms255×body80valid
20.0ms349×body80nan
0.0ms1×body160valid

simplify53.0ms

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: 0.1b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.1b
(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:
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
4.0ms
(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

prune126.0ms

Filtered
72 candidates to 43 candidates (59.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New70272
Fresh000
Picked101
Done000
Total71273

Merged error: 0.1b

Counts
73 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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:
6.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
3.0ms
(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))

series136.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
86.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms
(sqrt (atan2 b b))
11.0ms
(sqrt (atan2 b b))

simplify118.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0308751
1889651
24114639
35002636

prune220.0ms

Filtered
95 candidates to 60 candidates (63.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New93295
Fresh011
Picked101
Done000
Total94397

Merged error: 0.1b

Counts
97 → 3

localize15.0ms

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
(sqrt (atan2 b b))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series43.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
13.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify96.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 7 (28.0ms)

IterNodesCost
024212
127208
230208
335208
454208
5108208
6535208
71774204
85001204

prune213.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh022
Picked011
Done000
Total72375

Merged error: 0.1b

Counts
75 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow (atan2 b b) (* 1/2 (- b a)))
0.1b
(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-up
18×prod-diff
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×distribute-rgt-in distribute-lft-in
3×pow1 add-exp-log unpow-prod-down
2×expm1-log1p-u sub-neg add-cbrt-cube log1p-expm1-u add-log-exp
1×pow-to-exp pow-unpow pow-pow pow-exp sqr-pow
Counts
2 → 48
Calls
2 calls:
4.0ms
(pow (atan2 b b) (* 1/2 (- b a)))
5.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

series81.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(pow (atan2 b b) (* 1/2 (- b a)))
61.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify91.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0324582
1828448
23427428
35002401

prune66.0ms

Filtered
54 candidates to 26 candidates (48.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New54054
Fresh011
Picked011
Done011
Total54357

Merged error: 0.1b

Counts
57 → 3

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
01427
11427

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.9s1815×body5120exit
652.0ms7989×body80valid
581.0ms9961×body80nan
3.0ms1×body5120valid
3.0ms2×body2560valid
1.0ms2×body1280valid
1.0ms6×body160valid