Details

Time bar (total: 4.0s)

sample65.0ms

Algorithm
intervals
Results
21.0ms50×body10240exit
14.0ms255×body80valid
14.0ms300×body80nan
1.0ms1×body1280valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43155
516095
650015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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))

rewrite10.0ms

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)))
1.0ms
(sqrt (atan2 b b))

series94.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(pow (sqrt (atan2 b b)) (- b a))
60.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms
(sqrt (atan2 b b))

simplify45.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0148324
1412298
21346292
35001290

prune125.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

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)))

rewrite19.0ms

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))
10.0ms
(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)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
60.0ms
(sin (exp (log (pow (sqrt (atan2 b b)) (- b a)))))
10.0ms
(sqrt (atan2 b b))
54.0ms
(log (pow (sqrt (atan2 b b)) (- b a)))

simplify74.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0191563
1589513
22543499
35002499

prune207.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

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
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))))
6.0ms
(log (pow (cbrt (sqrt (atan2 b b))) (- b a)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
164.0ms
(log (cbrt (sqrt (atan2 b b))))
78.0ms
(log (pow (cbrt (sqrt (atan2 b b))) (- b a)))

simplify38.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (32.0ms)

IterNodesCost
0171548
1365501
21163501
35001487

prune281.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

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:
4.0ms
(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))

series139.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
89.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify68.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0201521
1574477
22332466
35001466

prune209.0ms

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

sample2.1s

Algorithm
intervals
Results
755.0ms1780×body10240exit
474.0ms9771×body80nan
461.0ms7997×body80valid
1.0ms1×body1280valid
0.0ms2×body320valid