Details

sample80.0ms

Algorithm

intervals

Results

28.0ms	60×	body	10240	exit
18.0ms	256×	body	80	valid
18.0ms	299×	body	80	nan

simplify52.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

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

series91.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
24.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sqrt (atan2 b b))

simplify76.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2702	425
3	5002	408

prune157.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
48×	`unpow-prod-up`
46×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`sqr-pow`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 171

Calls

4 calls:

9.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
41.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series148.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))

simplify63.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	451	2193
1	1880	1915
2	5002	1883

prune441.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt 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

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

Counts

4 → 58

Calls

4 calls:

0.0ms	(cbrt b)
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series206.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt b)
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify137.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	61	202
1	104	196
2	218	194
3	725	194
4	4173	194
5	5001	194

prune386.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	30
1	45	30
2	47	30
3	47	30

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	1838×	body	10240	exit
615.0ms	9911×	body	80	nan
577.0ms	7994×	body	80	valid
6.0ms	2×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid