Details

sample106.0ms

Algorithm

intervals

Results

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

simplify52.0ms

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	1609	5
6	5001	5

prune2.0ms

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

localize8.0ms

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

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:

4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
8.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series85.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1345	292
3	5001	290

prune102.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	2	58

Merged error: 0.0b

Counts

58 → 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))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`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 → 136

Calls

4 calls:

4.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
17.0ms	(* (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))

series143.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
36.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
9.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify54.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	280	1645
1	1169	1507
2	5001	1483

prune235.0ms

Filtered

148 candidates to 71 candidates (48.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Merged error: 0.0b

Counts

150 → 3

localize11.0ms

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))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
9×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow-pow` `sqrt-pow1`
4×	`unpow-prod-up` `add-exp-log`
3×	`pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 50

Calls

3 calls:

4.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
5.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
1.0ms	(sqrt (atan2 b b))

series120.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
72.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
13.0ms	(sqrt (atan2 b b))

simplify145.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	217	461
1	743	419
2	3884	391
3	5001	369

prune99.0ms

Filtered

59 candidates to 34 candidates (57.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	59	3	62

Merged error: 0.0b

Counts

62 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

258×	`sqrt-prod`
252×	`unpow-prod-down`
169×	`times-frac`
120×	`add-sqr-sqrt`
118×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqr-pow`
16×	`add-exp-log`
13×	`associate-/r` `associate-/l`
9×	`div-exp`
6×	`pow1` `pow-to-exp` `pow-exp` `add-cbrt-cube`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv` `pow-div`

Counts

4 → 249

Calls

4 calls:

13.0ms	(/ (pow (sqrt (sqrt (atan2 b b))) (* 2 b)) (pow (sqrt (sqrt (atan2 b b))) (* 2 a)))
17.0ms	(sin (/ (pow (sqrt (sqrt (atan2 b b))) (* 2 b)) (pow (sqrt (sqrt (atan2 b b))) (* 2 a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series282.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (pow (sqrt (sqrt (atan2 b b))) (* 2 b)) (pow (sqrt (sqrt (atan2 b b))) (* 2 a)))
160.0ms	(sin (/ (pow (sqrt (sqrt (atan2 b b))) (* 2 b)) (pow (sqrt (sqrt (atan2 b b))) (* 2 a))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify85.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	484	5165
1	2030	4846
2	5002	4824

prune478.0ms

Filtered

261 candidates to 121 candidates (46.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	261	3	264

Merged error: 0b

Counts

264 → 3

regimes38.0ms

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

sample3.3s

Algorithm

intervals

Results

1.8s	1774×	body	5120	exit
623.0ms	7990×	body	80	valid
555.0ms	9692×	body	80	nan
3.0ms	1×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	1280	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid