Details

sample107.0ms

Algorithm

intervals

Results

53.0ms	58×	body	5120	exit
20.0ms	256×	body	80	valid
17.0ms	306×	body	80	nan

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	1627	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: 0.1b

Counts

2 → 1

localize12.0ms

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))

rewrite14.0ms

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

series95.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
20.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(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	2702	425
3	5002	408

prune139.0ms

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

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))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
48×	`unpow-prod-up`
46×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`sqr-pow`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 171

Calls

4 calls:

3.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
22.0ms	(* (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))

series153.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
38.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms	(sqrt (atan2 b b))
15.0ms	(sqrt (atan2 b b))

simplify64.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	451	2193
1	1880	1915
2	5002	1883

prune385.0ms

Filtered

183 candidates to 96 candidates (52.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	182	3	185

Merged error: 0.0b

Counts

185 → 3

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
12×	`sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`unpow-prod-down`
7×	`pow1`
5×	`pow-pow` `sqrt-pow1`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 74

Calls

3 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
7.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
2.0ms	(sqrt (atan2 b b))

series124.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
82.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
11.0ms	(sqrt (atan2 b b))

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	893
1	1289	741
2	5002	695

prune153.0ms

Filtered

83 candidates to 43 candidates (51.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	84	2	86

Merged error: 0.0b

Counts

86 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b	(sin (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
0.0b	(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
12×	`sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`unpow-prod-down`
8×	`pow1`
5×	`add-exp-log` `pow-pow` `sqrt-pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`sub-neg` `expm1-udef`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `expm1-log1p` `pow-exp` `sin-diff` `sqrt-pow2` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sin (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
1.0ms	(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
2.0ms	(sqrt (atan2 b b))

series223.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
114.0ms	(sin (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
63.0ms	(expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
11.0ms	(sqrt (atan2 b b))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	416	1051
1	1309	887
2	5002	834

prune222.0ms

Filtered

98 candidates to 56 candidates (57.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Merged error: 0b

Counts

100 → 3

regimes41.0ms

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	11	7
1	11	7

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	1774×	body	5120	exit
787.0ms	7990×	body	80	valid
568.0ms	9692×	body	80	nan
3.0ms	1×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid