Details

Time bar (total: 4.5s)

sample332.0ms

Algorithm
intervals
Results
24.0ms50×body10240exit
16.0ms300×body80nan
15.0ms255×body80valid
1.0ms1×body1280valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43155
516095
650015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

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
10×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×pow1 unpow-prod-down sqrt-prod
5×pow-unpow
4×add-exp-log
3×pow-pow add-cbrt-cube add-log-exp
2×unpow-prod-up 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 → 48
Calls
3 calls:
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
4.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms
(sqrt (atan2 b b))

series111.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(pow (sqrt (atan2 b b)) (- b a))
73.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms
(sqrt (atan2 b b))

simplify40.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
0148325
1425298
21346292
35001290

prune137.0ms

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)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity
12×unpow-prod-down log-prod
11×add-cube-cbrt
9×sqrt-prod
7×pow1 add-exp-log
5×pow-unpow
4×unpow-prod-up add-cbrt-cube 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 → 72
Calls
4 calls:
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
8.0ms
(sin (exp (log (pow (sqrt (atan2 b b)) (- b a)))))
1.0ms
(sqrt (atan2 b b))
3.0ms
(log (pow (sqrt (atan2 b b)) (- b a)))

series152.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(pow (sqrt (atan2 b b)) (- b a))
62.0ms
(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)))

simplify76.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0191563
1589513
22543499
35002499

prune217.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

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)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
24×log-prod
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×cbrt-prod sqrt-prod
9×unpow-prod-down
7×pow1 add-exp-log
4×rem-log-exp add-cbrt-cube add-log-exp
3×log-pow
2×unpow-prod-up 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 → 72
Calls
4 calls:
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
1.0ms
(log (cbrt (sqrt (atan2 b b))))
4.0ms
(log (pow (cbrt (sqrt (atan2 b b))) (- b a)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(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)))

simplify39.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (33.0ms)

IterNodesCost
0171546
1365501
21163501
35001487

prune300.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

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))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
15×sqrt-prod
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
9×pow1 unpow-prod-down
6×sqrt-pow1
5×add-exp-log pow-unpow pow-pow
4×pow1/2 add-cbrt-cube add-log-exp
2×unpow-prod-up 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 → 66
Calls
4 calls:
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
9.0ms
(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))

series141.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(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))))
11.0ms
(sqrt (atan2 b b))
11.0ms
(sqrt (atan2 b b))

simplify71.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0201521
1574477
22332466
35001466

prune219.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes70.0ms

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

sample2.1s

Algorithm
intervals
Results
772.0ms1780×body10240exit
484.0ms7997×body80valid
478.0ms9771×body80nan
1.0ms1×body1280valid
0.0ms2×body320valid