Details

sample314.0ms

Algorithm

intervals

Results

23.0ms	48×	body	10240	exit
17.0ms	256×	body	80	valid
12.0ms	321×	body	80	nan

simplify60.0ms

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	1618	5
6	5001	5

prune4.0ms

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

localize11.0ms

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))

rewrite32.0ms

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:

5.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sqrt (atan2 b b))

series107.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sqrt (atan2 b b))

simplify78.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2697	425
3	5001	408

prune120.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	2	73

Merged error: 0.0b

Counts

73 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (* 1 (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

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:

9.0ms	(sin (* 1 (pow (sqrt (atan2 b b)) (- b a))))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series95.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(sin (* 1 (pow (sqrt (atan2 b b)) (- b a))))
20.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify80.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	258	526
1	759	442
2	2965	434
3	5001	417

prune122.0ms

Filtered

72 candidates to 44 candidates (61.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	72	2	74

Merged error: 0.0b

Counts

74 → 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))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`sqrt-prod`
78×	`unpow-prod-down`
52×	`add-cube-cbrt`
48×	`unpow-prod-up`
46×	`pow-unpow`
44×	`pow-pow`
39×	`pow1`
36×	`sqrt-pow1` `prod-diff`
32×	`swap-sqr`
25×	`pow-prod-up` `unswap-sqr`
24×	`associate-r` `associate-l`
20×	`pow1/2`
19×	`pow-prod-down`
16×	`add-exp-log`
15×	`pow-sqr`
14×	`distribute-lft-out--` `sqr-pow`
10×	`sqrt-pow2`
9×	`prod-exp`
6×	`pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `pow-sub` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `*-commutative` `cbrt-unprod`

Counts

4 → 228

Calls

4 calls:

25.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
35.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series152.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(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)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify95.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	615	2319
1	2731	2061
2	5001	2033

prune373.0ms

Filtered

240 candidates to 111 candidates (46.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	239	1	240
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	241	1	242

Merged error: 0.0b

Counts

242 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 1))
1.0b	(sqrt (atan2 b b))

rewrite12.0ms

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:

9.0ms	(sin (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 1))
2.0ms	(sqrt (atan2 b b))

series90.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(sin (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 1))
11.0ms	(sqrt (atan2 b b))

simplify37.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	94	194
1	232	175
2	884	169
3	5002	167

prune84.0ms

Filtered

30 candidates to 24 candidates (80.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	1	31

Merged error: 0.0b

Counts

31 → 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

791.0ms	1823×	body	10240	exit
451.0ms	7992×	body	80	valid
373.0ms	9852×	body	80	nan
3.0ms	1×	body	5120	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	640	valid
0.0ms	3×	body	160	valid