Details

sample314.0ms

Algorithm

intervals

Results

20.0ms	38×	body	10240	exit
16.0ms	256×	body	80	valid
13.0ms	275×	body	80	nan

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(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:

6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series107.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
31.0ms	(pow (sqrt (atan2 b b)) (- b a))
16.0ms	(sqrt (atan2 b b))

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	255	515
1	727	433
2	2662	425
3	5001	408

prune150.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series76.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify83.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	264	1026
1	731	882
2	2885	870
3	5002	838

prune297.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
3.0b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`log-prod` `sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
9×	`pow1`
7×	`add-exp-log`
6×	`sqrt-pow1`
5×	`pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `pow-sub` `sqr-pow`
1×	`log-div` `log-pow` `sqrt-pow2` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
5.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
82.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify117.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	345	1080
1	985	903
2	3991	894
3	5001	893

prune341.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

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))

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify97.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 7 (28.0ms)

Iter	Nodes	Cost
0	24	212
1	27	208
2	30	208
3	35	208
4	54	208
5	108	208
6	535	208
7	1774	204
8	5001	204

prune243.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes91.0ms

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	14
1	12	14

end0.0ms

sample2.1s

Algorithm

intervals

Results

810.0ms	1837×	body	10240	exit
476.0ms	7995×	body	80	valid
459.0ms	9862×	body	80	nan
3.0ms	1×	body	5120	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid