Details

sample63.0ms

Algorithm

intervals

Results

18.0ms	48×	body	10240	exit
16.0ms	256×	body	80	valid
14.0ms	320×	body	80	nan

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

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))

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	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series91.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify45.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1345	292
3	5001	290

prune127.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`unpow-prod-down` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`unpow-prod-up` `add-cbrt-cube` `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 → 92

Calls

4 calls:

4.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
4.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series77.0ms

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))

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	160	630
1	454	596
2	1640	588
3	5002	584

prune270.0ms

Filtered

104 candidates to 62 candidates (59.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
2.7b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
18×	`add-sqr-sqrt` `unpow-prod-down`
16×	`*-un-lft-identity`
15×	`log-prod`
14×	`add-cube-cbrt`
9×	`pow1`
7×	`add-exp-log`
6×	`sqrt-pow1`
5×	`pow-unpow` `pow-pow`
4×	`unpow-prod-up` `pow1/2` `add-cbrt-cube` `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 → 86

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))
3.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series132.0ms

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))
81.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify74.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	214	664
1	636	607
2	2696	601
3	5002	601

prune285.0ms

Filtered

98 candidates to 57 candidates (58.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
2.7b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))
2.7b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
24×	`sqrt-prod`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log`
6×	`pow1` `rem-log-exp`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `pow-exp` `log-pow` `pow-sub` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

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

series182.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
81.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))
81.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify300.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	161	698
1	334	626
2	1053	622
3	4980	614
4	5002	614

prune312.0ms

Filtered

92 candidates to 58 candidates (63.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes46.0ms

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	11	16

end0.0ms

sample2.1s

Algorithm

intervals

Results

806.0ms	1918×	body	10240	exit
464.0ms	9919×	body	80	nan
428.0ms	7987×	body	80	valid
5.0ms	4×	body	2560	valid
1.0ms	4×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid