Details

sample75.0ms

Algorithm

intervals

Results

23.0ms	57×	body	10240	exit
19.0ms	334×	body	80	nan
14.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify53.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

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

series69.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify67.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 6 (64.0ms)

Iter	Nodes	Cost
0	65	150
1	112	137
2	200	132
3	372	131
4	681	131
5	2254	131
6	5001	130

prune74.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* (cos 1) (log (sqrt (atan2 b b)))) (- b a) (sin 1))
1.0b	(* (cos 1) (log (sqrt (atan2 b b))))
1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
11×	`pow1`
7×	`add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `associate-l`
1×	`rem-sqrt-square` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (* (cos 1) (log (sqrt (atan2 b b)))) (- b a) (sin 1))
8.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(log (sqrt (atan2 b b)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(fma (* (cos 1) (log (sqrt (atan2 b b)))) (- b a) (sin 1))
157.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
10.0ms	(sqrt (atan2 b b))
65.0ms	(log (sqrt (atan2 b b)))

simplify131.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	152	636
1	487	554
2	1554	539
3	4729	539
4	5001	539

prune208.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a) (sin 1))
1.0b	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
1.0b	(sqrt (atan2 b b))
2.0b	(log (log (exp (sqrt (atan2 b b)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
23×	`log-pow`
19×	`add-sqr-sqrt`
18×	`exp-prod`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `sqrt-prod`
10×	`distribute-rgt-in` `distribute-lft-in`
7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a) (sin 1))
7.0ms	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (log (exp (sqrt (atan2 b b)))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a) (sin 1))
159.0ms	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
10.0ms	(sqrt (atan2 b b))
70.0ms	(log (log (exp (sqrt (atan2 b b)))))

simplify133.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	180	862
1	533	717
2	1442	684
3	4670	684
4	5001	684

prune255.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
2.0b	(log (log (exp (sqrt (atan2 b b)))))
2.0b	(log (log (exp (sqrt (atan2 b b)))))
2.0b	(log (log (exp (sqrt (atan2 b b)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
24×	`log-pow`
18×	`exp-prod`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
11×	`pow1`
7×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
2.0ms	(log (log (exp (sqrt (atan2 b b)))))
2.0ms	(log (log (exp (sqrt (atan2 b b)))))
3.0ms	(log (log (exp (sqrt (atan2 b b)))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (atan2 b b))
67.0ms	(log (log (exp (sqrt (atan2 b b)))))
66.0ms	(log (log (exp (sqrt (atan2 b b)))))
71.0ms	(log (log (exp (sqrt (atan2 b b)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 7 (86.0ms)

Iter	Nodes	Cost
0	65	545
1	89	466
2	118	466
3	156	466
4	285	466
5	767	466
6	3559	465
7	5001	459

prune370.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes77.0ms

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	7	5

end0.0ms

sample2.1s

Algorithm

intervals

Results

755.0ms	1762×	body	10240	exit
461.0ms	9778×	body	80	nan
459.0ms	7990×	body	80	valid
6.0ms	2×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	1×	body	1280	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid