Details

sample76.0ms

Algorithm

intervals

Results

24.0ms	52×	body	10240	exit
18.0ms	302×	body	80	nan
18.0ms	255×	body	80	valid
0.0ms	1×	body	320	valid

simplify50.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite9.0ms

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))

series89.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(pow (sqrt (atan2 b b)) (- b a))
56.0ms	(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 (39.0ms)

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

prune123.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.2b	(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

2.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
4.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series80.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
60.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify55.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	145	236
1	453	212
2	1901	202
3	5001	199

prune72.0ms

Pruning

3 alts after pruning (2 fresh and 1 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))
0.2b	(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))

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))
8.0ms	(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))

series136.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(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))

simplify67.0ms

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

prune209.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
4.3b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod` `sqrt-prod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
6×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp`
2×	`unpow-prod-up` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `log-div` `pow-exp` `log-pow` `pow-sub` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

14.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
4.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series188.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
81.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	204	575
1	466	508
2	1757	499
3	5001	499

prune223.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes35.0ms

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	14	11
1	14	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

991.0ms	1864×	body	10240	exit
612.0ms	9960×	body	80	nan
580.0ms	7992×	body	80	valid
9.0ms	3×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid