Details

sample72.0ms

Algorithm

intervals

Results

29.0ms	71×	body	10240	exit
14.0ms	255×	body	80	valid
13.0ms	293×	body	80	nan
0.0ms	1×	body	640	valid

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	321	5
5	1618	5
6	5001	5

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite13.0ms

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	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series93.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (sqrt (atan2 b b)) (- b a))
63.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(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	2698	425
3	5002	408

prune119.0ms

Filtered

72 candidates to 43 candidates (40.3%)

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: 0.2b

Counts

73 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.2b	(sin (* (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))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`pow1` `unpow-prod-down` `prod-diff`
6×	`sqrt-pow1`
5×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
22.0ms	(sin (* (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))

series141.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
90.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify118.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	308	751
1	889	651
2	4109	639
3	5002	621

prune207.0ms

Filtered

95 candidates to 59 candidates (37.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Merged error: 0.2b

Counts

98 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b	(pow (atan2 b b) (* 1/4 (- b a)))
0.2b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* 1/4 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`unpow-prod-up`
31×	`add-cube-cbrt`
27×	`prod-diff`
19×	`pow-unpow`
12×	`unpow-prod-down` `sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
6×	`add-exp-log` `pow-pow`
5×	`sqrt-pow1` `associate-r`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sub-neg` `pow1/2` `associate-l`
2×	`pow-to-exp` `pow-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`rem-sqrt-square` `*-commutative` `sqrt-pow2` `pow-sub` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
8.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
23.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* 1/4 (- b a)))))
2.0ms	(sqrt (atan2 b b))

series201.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
20.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
142.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* 1/4 (- b a)))))
11.0ms	(sqrt (atan2 b b))

simplify58.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	604	1245
1	2035	1031
2	5001	997

prune402.0ms

Filtered

132 candidates to 74 candidates (43.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Merged error: 0.2b

Counts

136 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (atan2 b b) (* 1/4 (- b a)))
0.2b	(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (* 1/4 (- b a)))))
1.0b	(sqrt (atan2 b b))
5.7b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
33×	`unpow-prod-up`
32×	`add-cube-cbrt`
27×	`prod-diff`
24×	`log-prod`
19×	`pow-unpow`
13×	`log-pow`
12×	`unpow-prod-down` `sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1`
7×	`add-exp-log`
6×	`pow-pow`
5×	`sqrt-pow1` `associate-r`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sub-neg` `pow1/2` `rem-log-exp` `associate-l`
2×	`pow-to-exp` `pow-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`rem-sqrt-square` `log-div` `*-commutative` `sqrt-pow2` `pow-sub` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

8.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
29.0ms	(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (* 1/4 (- b a)))))
2.0ms	(sqrt (atan2 b b))
10.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
136.0ms	(sin (* (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))) (pow (atan2 b b) (* 1/4 (- b a)))))
10.0ms	(sqrt (atan2 b b))
84.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	659	1379
1	1951	1131
2	5001	1102

prune322.0ms

Filtered

138 candidates to 83 candidates (39.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	138	3	141

Merged error: 0.2b

Counts

141 → 3

regimes39.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

end0.0ms

sample2.0s

Algorithm

intervals

Results

829.0ms	1899×	body	10240	exit
455.0ms	7987×	body	80	valid
377.0ms	9990×	body	80	nan
9.0ms	3×	body	5120	valid
2.0ms	2×	body	2560	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	640	valid
0.0ms	2×	body	160	valid