Details

sample72.0ms

Algorithm

intervals

Results

19.0ms	54×	body	10240	exit
18.0ms	346×	body	80	nan
14.0ms	256×	body	80	valid

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	321	5
5	1627	5
6	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

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))

rewrite23.0ms

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:

12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
8.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series97.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
26.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (68.0ms)

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

prune145.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0b	(pow (atan2 b b) (* 1/2 (- b a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
18×	`prod-diff`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`distribute-rgt-in` `distribute-lft-in`
3×	`pow1` `add-exp-log` `unpow-prod-down`
2×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 48

Calls

2 calls:

18.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
10.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series88.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
23.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify99.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	324	582
1	913	448
2	3678	428
3	5001	425

prune92.0ms

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	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0b	(exp (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.3b	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`pow1`
6×	`add-exp-log` `log-prod`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `exp-sum`
2×	`sub-neg` `log-pow`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `rem-log-exp` `pow-exp` `rem-exp-log` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

20.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
14.0ms	(exp (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
8.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
12.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

series242.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
66.0ms	(exp (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
22.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
93.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	383	909
1	1067	734
2	4282	697
3	5001	693

prune202.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0b	(pow E (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.3b	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

25×	`unpow-prod-up`
21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1`
7×	`add-exp-log`
6×	`unpow-prod-down` `log-prod`
5×	`pow-unpow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-exp`
2×	`pow-to-exp` `sub-neg` `pow-pow` `log-pow` `sqr-pow`
1×	`e-exp-1` `rem-log-exp`

Counts

4 → 86

Calls

4 calls:

17.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
14.0ms	(pow E (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
7.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
15.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
108.0ms	(pow E (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
22.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
91.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	429	1023
1	1356	851
2	5001	830

prune225.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

728.0ms	1741×	body	10240	exit
494.0ms	9997×	body	80	nan
471.0ms	7991×	body	80	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	640	valid