Details

sample68.0ms

Algorithm

intervals

Results

21.0ms	52×	body	10240	exit
16.0ms	255×	body	80	valid
13.0ms	296×	body	80	nan
0.0ms	1×	body	640	valid

simplify53.0ms

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: 0.2b

localize9.0ms

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))

rewrite18.0ms

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:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series97.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(pow (sqrt (atan2 b b)) (- b a))
65.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(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

prune126.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
0.2b	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`pow-unpow`
17×	`add-cube-cbrt`
15×	`times-frac`
9×	`sqrt-prod`
8×	`pow1`
6×	`unpow-prod-down`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-pow` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `div-sub` `pow-exp` `sqrt-pow2` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

11.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
30.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series132.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
85.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify87.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	257	573
1	807	532
2	3637	517
3	5001	513

prune230.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (fabs (cbrt (atan2 b b))) (sqrt (cbrt (atan2 b b))))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
10×	`cbrt-prod`
9×	`associate-r`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 61

Calls

4 calls:

11.0ms	(* (fabs (cbrt (atan2 b b))) (sqrt (cbrt (atan2 b b))))
1.0ms	(cbrt (atan2 b b))
1.0ms	(cbrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series348.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (fabs (cbrt (atan2 b b))) (sqrt (cbrt (atan2 b b))))
104.0ms	(cbrt (atan2 b b))
107.0ms	(cbrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify47.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	115	428
1	396	397
2	1305	390
3	5001	385

prune238.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes78.0ms

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	17	17
1	17	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

753.0ms	1795×	body	10240	exit
575.0ms	9659×	body	80	nan
458.0ms	7992×	body	80	valid
4.0ms	3×	body	2560	valid
2.0ms	3×	body	1280	valid
0.0ms	2×	body	160	valid