Details

sample321.0ms

Algorithm

intervals

Results

31.0ms	72×	body	10240	exit
16.0ms	256×	body	80	valid
12.0ms	348×	body	80	nan

simplify57.0ms

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

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

rewrite31.0ms

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:

18.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series102.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(pow (sqrt (atan2 b b)) (- b a))
60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms	(sqrt (atan2 b b))

simplify76.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2703	425
3	5001	408

prune152.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0b

Counts

73 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

42×	`exp-prod`
26×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
22×	`unpow-prod-up` `log-pow`
18×	`prod-diff`
12×	`unpow-prod-down`
9×	`sqrt-prod`
6×	`pow1` `log-prod`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sin-sum`
2×	`sub-neg` `rem-log-exp` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-exp-log`

Counts

4 → 94

Calls

4 calls:

8.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
6.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
7.0ms	(exp (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series119.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
19.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
34.0ms	(exp (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify62.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	292	800
1	679	676
2	2202	661
3	5001	612

prune264.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	107	2	109

Merged error: 0b

Counts

109 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a)))
0.0b	(log (exp (pow (* (sqrt (sqrt (atan2 b b))) (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

138×	`sqrt-prod`
124×	`exp-prod`
109×	`add-sqr-sqrt`
94×	`unpow-prod-down`
63×	`log-pow`
47×	`add-cube-cbrt` `*-un-lft-identity`
30×	`swap-sqr`
22×	`unpow-prod-up`
18×	`associate-r` `associate-l` `prod-diff` `unswap-sqr`
7×	`pow1`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `*-commutative` `sqr-pow`
1×	`rem-exp-log`

Counts

4 → 179

Calls

4 calls:

22.0ms	(exp (pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a)))
19.0ms	(log (exp (pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series77.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(exp (pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a)))
19.0ms	(log (exp (pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify72.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	379	1546
1	969	1250
2	2933	1222
3	5001	1172

prune424.0ms

Filtered

191 candidates to 95 candidates (49.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	191	2	193

Merged error: 0b

Counts

193 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series43.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify99.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 7 (28.0ms)

Iter	Nodes	Cost
0	24	212
1	27	208
2	30	208
3	35	208
4	54	208
5	108	208
6	535	208
7	1774	204
8	5001	204

prune283.0ms

Filtered

72 candidates to 48 candidates (66.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0b

Counts

74 → 2

regimes36.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

769.0ms	1803×	body	10240	exit
444.0ms	7988×	body	80	valid
338.0ms	9775×	body	80	nan
3.0ms	2×	body	2560	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid