Details

Time bar (total: 4.5s)

sample320.0ms

Algorithm
intervals
Results
22.0ms51×body10240exit
15.0ms255×body80valid
14.0ms306×body80nan
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: 0.3b

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))

rewrite29.0ms

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:
7.0ms
(pow (sqrt (atan2 b b)) (- b a))
9.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms
(sqrt (atan2 b b))

series95.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(pow (sqrt (atan2 b b)) (- b a))
59.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms
(sqrt (atan2 b b))

simplify52.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0148324
1412298
21346292
35001290

prune123.0ms

Pruning

2 alts after pruning (2 fresh and 0 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))
0.2b
(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))

rewrite40.0ms

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:
8.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
29.0ms
(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))

series128.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
84.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
9.0ms
(sqrt (atan2 b b))
9.0ms
(sqrt (atan2 b b))

simplify68.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0201524
1606477
22337466
35001466

prune211.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))))
0.3b
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
33×unpow-prod-down
24×sqrt-prod
17×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity cube-prod
6×pow1
4×unpow-prod-up add-exp-log add-cbrt-cube add-log-exp
3×sqr-pow
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×cube-div cube-mult cbrt-div pow1/3 unpow3 rem-cbrt-cube pow-sub
Counts
4 → 79
Calls
4 calls:
35.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))))
11.0ms
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series133.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))))
26.0ms
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
10.0ms
(sqrt (atan2 b b))
13.0ms
(sqrt (atan2 b b))

simplify100.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0307782
11014729
23748718
35001718

prune230.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b
(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
29×sqrt-prod
21×add-sqr-sqrt
19×*-un-lft-identity
18×unpow-prod-down
15×add-cube-cbrt
13×pow-unpow
12×pow1
10×pow-pow sqrt-pow1
6×add-exp-log pow1/2
4×add-cbrt-cube add-log-exp
2×unpow-prod-up pow-to-exp rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- difference-of-squares sqr-pow
1×sub-neg pow-sub
Counts
4 → 92
Calls
4 calls:
8.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms
(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series253.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
207.0ms
(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
9.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify38.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0339771
11115720
25001678

prune305.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes44.0ms

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
01314
11314

end0.0ms

sample2.2s

Algorithm
intervals
Results
772.0ms1896×body10240exit
454.0ms9745×body80nan
444.0ms7993×body80valid
2.0ms1×body5120valid
1.0ms2×body1280valid
1.0ms1×body2560valid
0.0ms2×body320valid
0.0ms1×body160valid