Details

sample71.0ms

Algorithm

intervals

Results

30.0ms	71×	body	10240	exit
15.0ms	255×	body	80	valid
11.0ms	293×	body	80	nan
0.0ms	1×	body	640	valid

simplify50.0ms

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

prune5.0ms

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

localize9.0ms

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))

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:

5.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series95.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (sqrt (atan2 b b)) (- b a))
65.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(sqrt (atan2 b b))

simplify45.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1342	292
3	5002	290

prune103.0ms

Filtered

57 candidates to 36 candidates (36.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 0.2b

Counts

58 → 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))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`pow1` `unpow-prod-down`
6×	`sqrt-pow1`
5×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `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 → 66

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
15.0ms	(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))

series142.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
93.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify70.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	201	521
1	574	477
2	2328	466
3	5001	466

prune179.0ms

Filtered

78 candidates to 50 candidates (35.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0.2b

Counts

81 → 4

localize15.0ms

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))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`pow-unpow`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`unpow-prod-down` `sqrt-prod`
9×	`pow1`
6×	`unpow-prod-up` `add-exp-log` `pow-pow`
5×	`sqrt-pow1` `associate-r`
4×	`add-cbrt-cube` `add-log-exp`
3×	`sub-neg` `pow1/2` `associate-l`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`rem-sqrt-square` `*-commutative` `sqrt-pow2` `pow-sub` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
7.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
11.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* 1/4 (- b a)))))
2.0ms	(sqrt (atan2 b b))

series199.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
20.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
140.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* 1/4 (- b a)))))
11.0ms	(sqrt (atan2 b b))

simplify45.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	372	691
1	1315	642
2	5001	618

prune222.0ms

Filtered

97 candidates to 62 candidates (36.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Merged error: 0.2b

Counts

101 → 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)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`pow-unpow`
18×	`*-un-lft-identity`
15×	`log-prod`
14×	`add-cube-cbrt`
13×	`log-pow`
12×	`unpow-prod-down` `sqrt-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`unpow-prod-up` `pow-pow`
5×	`sqrt-pow1` `associate-r`
4×	`add-cbrt-cube` `add-log-exp`
3×	`sub-neg` `pow1/2` `rem-log-exp` `associate-l`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `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 → 91

Calls

4 calls:

6.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
18.0ms	(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)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (atan2 b b) (* 1/4 (- b a)))
135.0ms	(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))
85.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify40.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	403	801
1	1211	729
2	5002	708

prune278.0ms

Filtered

103 candidates to 70 candidates (32.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	103	3	106

Merged error: 0.2b

Counts

106 → 3

regimes40.0ms

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

sample2.3s

Algorithm

intervals

Results

1.0s	1899×	body	10240	exit
481.0ms	7987×	body	80	valid
390.0ms	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