Details

Time bar (total: 4.5s)

sample63.0ms

Algorithm
intervals
Results
21.0ms50×body10240exit
14.0ms255×body80valid
13.0ms300×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: 0.2b

localize8.0ms

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))

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))

series95.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(pow (sqrt (atan2 b b)) (- b a))
64.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms
(sqrt (atan2 b b))

simplify75.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0255514
1714433
22703425
35001408

prune153.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (atan2 b b)) (- b a))
0.2b
(sin (exp (log (pow (sqrt (atan2 b b)) (- b a)))))
1.0b
(sqrt (atan2 b b))
4.6b
(log (pow (sqrt (atan2 b b)) (- b a)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×*-un-lft-identity
23×add-cube-cbrt
22×unpow-prod-up
21×log-prod
18×prod-diff
12×unpow-prod-down
9×sqrt-prod
7×pow1 add-exp-log
5×pow-unpow
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-pow rem-log-exp
2×pow-to-exp sub-neg sqrt-pow1 pow1/2 pow-exp pow-sub sqr-pow
1×rem-sqrt-square log-div log-pow sqrt-pow2 distribute-lft-out-- difference-of-squares
Counts
4 → 98
Calls
4 calls:
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
11.0ms
(sin (exp (log (pow (sqrt (atan2 b b)) (- b a)))))
1.0ms
(sqrt (atan2 b b))
4.0ms
(log (pow (sqrt (atan2 b b)) (- b a)))

series147.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
59.0ms
(sin (exp (log (pow (sqrt (atan2 b b)) (- b a)))))
10.0ms
(sqrt (atan2 b b))
59.0ms
(log (pow (sqrt (atan2 b b)) (- b a)))

simplify122.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0325949
1964774
23988762
35001760

prune267.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
3.2b
(log (cbrt (sqrt (atan2 b b))))
4.7b
(log (pow (cbrt (sqrt (atan2 b b))) (- b a)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
33×log-prod
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
12×cbrt-prod sqrt-prod
11×unpow-prod-up
9×unpow-prod-down prod-diff
7×pow1 add-exp-log
4×expm1-log1p-u rem-log-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×log-pow
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-to-exp sub-neg log-div pow1/3 pow-exp pow-sub sqr-pow
Counts
4 → 89
Calls
4 calls:
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
1.0ms
(log (cbrt (sqrt (atan2 b b))))
5.0ms
(log (pow (cbrt (sqrt (atan2 b b))) (- b a)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
173.0ms
(log (cbrt (sqrt (atan2 b b))))
84.0ms
(log (pow (cbrt (sqrt (atan2 b b))) (- b a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0303782
1718669
22423660
35001631

prune335.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.3b
(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))

rewrite18.0ms

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:
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
8.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series139.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
91.0ms
(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

prune255.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes62.0ms

Accuracy

0% (0.0b 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
097

end0.0ms

sample2.2s

Algorithm
intervals
Results
910.0ms1780×body10240exit
457.0ms7997×body80valid
454.0ms9771×body80nan
1.0ms1×body1280valid
0.0ms2×body320valid