Details

sample64.0ms

Algorithm

intervals

Results

21.0ms	48×	body	10240	exit
15.0ms	256×	body	80	valid
12.0ms	321×	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	315	5
5	1600	5
6	5001	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

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))

rewrite10.0ms

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:

3.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series99.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
27.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1341	292
3	5002	290

prune102.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	2	58

Merged error: 0.0b

Counts

58 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (pow (sqrt (atan2 b b)) (- b a)) 1))
0.0b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite11.0ms

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 (pow (sqrt (atan2 b b)) (- b a)) 1))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series94.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(sin (pow (pow (sqrt (atan2 b b)) (- b a)) 1))
20.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sqrt (atan2 b b))

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	152	334
1	453	305
2	1543	299
3	5002	297

prune109.0ms

Filtered

57 candidates to 37 candidates (64.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	57	2	59

Merged error: 0.0b

Counts

59 → 2

localize11.0ms

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))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
64×	`*-un-lft-identity`
46×	`pow-unpow`
44×	`pow-pow`
39×	`pow1`
36×	`sqrt-pow1`
28×	`add-cube-cbrt`
25×	`pow-prod-up` `unswap-sqr`
23×	`swap-sqr`
20×	`pow1/2`
19×	`pow-prod-down`
16×	`add-exp-log`
15×	`associate-r` `associate-l` `pow-sqr`
14×	`distribute-lft-out--` `sqr-pow`
12×	`unpow-prod-up`
10×	`sqrt-pow2`
9×	`prod-exp`
6×	`pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube` `difference-of-squares`
4×	`pow-sub` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `*-commutative` `cbrt-unprod`

Counts

4 → 193

Calls

4 calls:

14.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
26.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series156.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
39.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
14.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify73.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	435	1771
1	1889	1651
2	5001	1623

prune272.0ms

Filtered

205 candidates to 85 candidates (41.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	206	1	207

Merged error: 0.0b

Counts

207 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (pow (sqrt (sqrt (atan2 b b))) 1) (* 2 (- 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` `add-cbrt-cube` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

2 → 20

Calls

2 calls:

5.0ms	(sin (pow (pow (sqrt (sqrt (atan2 b b))) 1) (* 2 (- b a))))
1.0ms	(sqrt (atan2 b b))

series90.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(sin (pow (pow (sqrt (sqrt (atan2 b b))) 1) (* 2 (- b a))))
13.0ms	(sqrt (atan2 b b))

simplify35.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	89	170
1	222	152
2	833	145
3	5001	145

prune72.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	1	27

Merged error: 0.0b

Counts

27 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample2.0s

Algorithm

intervals

Results

806.0ms	1823×	body	10240	exit
462.0ms	7992×	body	80	valid
364.0ms	9852×	body	80	nan
3.0ms	1×	body	5120	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	640	valid
1.0ms	3×	body	160	valid