Details

sample315.0ms

Algorithm

intervals

Results

23.0ms	50×	body	10240	exit
15.0ms	300×	body	80	nan
14.0ms	255×	body	80	valid
1.0ms	1×	body	1280	valid

simplify56.0ms

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	321	5
5	1627	5
6	5001	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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))

rewrite16.0ms

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)))
3.0ms	(sqrt (atan2 b b))

series111.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
65.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
27.0ms	(sqrt (atan2 b b))

simplify68.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	255	515
1	727	433
2	2663	425
3	5001	408

prune157.0ms

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)))

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)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(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)))

simplify124.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	325	949
1	964	774
2	3988	762
3	5001	760

prune272.0ms

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

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)))

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)))

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	303	780
1	718	669
2	2423	660
3	5001	631

prune334.0ms

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))

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))
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:

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))

simplify122.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	308	751
1	889	651
2	4114	639
3	5002	636

prune256.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes68.0ms

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)

Iter	Nodes	Cost
0	9	7

end0.0ms

sample2.0s

Algorithm

intervals

Results

743.0ms	1780×	body	10240	exit
466.0ms	9771×	body	80	nan
444.0ms	7997×	body	80	valid
1.0ms	1×	body	1280	valid
0.0ms	2×	body	320	valid