Details

sample71.0ms

Algorithm

intervals

Results

18.0ms	54×	body	10240	exit
17.0ms	256×	body	80	valid
16.0ms	346×	body	80	nan

simplify51.0ms

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: 0.0b

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))

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:

9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series98.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(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	1345	292
3	5001	290

prune130.0ms

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)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

11.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
4.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
23.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	145	236
1	453	212
2	1900	202
3	5001	199

prune69.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `log-prod`
4×	`unpow-prod-up` `exp-prod` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `exp-sum`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `log-pow`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `rem-log-exp` `pow-exp` `rem-exp-log` `sqr-pow`

Counts

4 → 53

Calls

4 calls:

11.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
11.0ms	(exp (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
4.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
12.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(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)))
95.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	199	537
1	590	474
2	2349	445
3	5001	438

prune158.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

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)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

11.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
11.0ms	(pow E (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
4.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
9.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
107.0ms	(pow E (log (sin (pow (atan2 b b) (* 1/2 (- b a))))))
27.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
93.0ms	(log (sin (pow (atan2 b b) (* 1/2 (- b a)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	245	647
1	845	587
2	3628	564
3	5001	563

prune186.0ms

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

sample2.3s

Algorithm

intervals

Results

706.0ms	1741×	body	10240	exit
627.0ms	9997×	body	80	nan
447.0ms	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