Details

sample84.0ms

Algorithm

intervals

Results

32.0ms	62×	body	10240	exit
15.0ms	332×	body	80	nan
14.0ms	254×	body	80	valid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	315	5
5	1609	5
6	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.4b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite20.0ms

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))
10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series88.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(pow (sqrt (atan2 b b)) (- b a))
60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify44.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1346	292
3	5001	290

prune138.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.5b	(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))

rewrite46.0ms

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:

11.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
31.0ms	(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))

series132.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(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))
10.0ms	(sqrt (atan2 b b))

simplify69.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	201	521
1	574	477
2	2332	466
3	5001	466

prune237.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

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))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

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

series42.0ms

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))

simplify86.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 7 (27.0ms)

Iter	Nodes	Cost
0	22	188
1	25	184
2	28	184
3	33	184
4	52	184
5	106	184
6	533	184
7	1765	180
8	5001	180

prune246.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

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))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify96.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 7 (27.0ms)

Iter	Nodes	Cost
0	22	192
1	25	188
2	28	188
3	33	188
4	52	188
5	106	188
6	533	184
7	1765	180
8	5001	180

prune240.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes53.0ms

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)

Iter	Nodes	Cost
0	16	25
1	16	25

end0.0ms

sample2.2s

Algorithm

intervals

Results

773.0ms	1786×	body	10240	exit
462.0ms	9625×	body	80	nan
454.0ms	7992×	body	80	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	640	valid
1.0ms	1×	body	1280	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid