Details

sample310.0ms

Algorithm

intervals

Results

17.0ms	331×	body	80	nan
14.0ms	256×	body	80	valid
2.0ms	53×	body	80	overflowed

simplify57.0ms

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: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

series110.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(pow (sqrt (atan2 b b)) (- b a))
74.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(sqrt (atan2 b b))

simplify69.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

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

prune156.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
0.0b	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log` `add-sqr-sqrt`
16×	`pow-exp`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff` `prod-exp`
7×	`pow1` `pow-to-exp`
6×	`sqrt-prod`
5×	`pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow1/2`
1×	`pow2` `sub-neg` `unpow-prod-down` `sqrt-unprod` `pow-prod-down` `pow-sqr` `pow-prod-up` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

8.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
7.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series100.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
61.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify143.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	276	831
1	750	629
2	3971	600
3	5001	598

prune221.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 (log1p (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))))
0.0b	(expm1 (log1p (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 51

Calls

4 calls:

1.0ms	(sin (expm1 (log1p (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))))
0.0ms	(expm1 (log1p (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series161.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sin (expm1 (log1p (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))))
50.0ms	(expm1 (log1p (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify80.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (20.0ms)

Iter	Nodes	Cost
0	106	484
1	208	424
2	634	398
3	2217	389
4	5001	389

prune210.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes34.0ms

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	12	12

end0.0ms

sample1.4s

Algorithm

intervals

Results

458.0ms	7993×	body	80	valid
458.0ms	9890×	body	80	nan
79.0ms	1801×	body	80	overflowed
61.0ms	24×	body	10240	exit
6.0ms	2×	body	5120	valid
2.0ms	3×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid