Details

sample309.0ms

Algorithm

intervals

Results

19.0ms	52×	body	10240	exit
15.0ms	256×	body	80	valid
13.0ms	308×	body	80	nan

simplify58.0ms

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

rewrite20.0ms

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:

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

series110.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
31.0ms	(sqrt (atan2 b b))

simplify82.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2702	425
3	5002	408

prune124.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 206

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
23.0ms	(* (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))

series89.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(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)))
14.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify67.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	461	2471
1	2064	2166
2	5001	2132

prune396.0ms

Filtered

218 candidates to 111 candidates (50.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	217	3	220

Merged error: 0.0b

Counts

220 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.0b	(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	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
2.0ms	(sqrt (atan2 b b))

series116.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
30.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify46.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	398	893
1	1289	741
2	5001	695

prune136.0ms

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

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
0.0b	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3))
1.0b	(sqrt (atan2 b b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

115×	`unpow-prod-down`
110×	`unpow-prod-up`
90×	`prod-diff`
87×	`add-sqr-sqrt`
86×	`add-cube-cbrt` `*-un-lft-identity`
76×	`cbrt-prod`
70×	`cube-prod`
55×	`distribute-rgt-in` `distribute-lft-in`
48×	`sqrt-prod`
10×	`sub-neg`
8×	`pow1`
7×	`add-exp-log` `sqr-pow`
6×	`pow-pow`
5×	`sqrt-pow1` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow1/2`
2×	`cube-mult` `unpow3`
1×	`rem-sqrt-square` `pow1/3` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 243

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
11.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
13.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3))
2.0ms	(sqrt (atan2 b b))

series128.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
51.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
36.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3))
10.0ms	(sqrt (atan2 b b))

simplify90.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	740	3734
1	2453	3110
2	5001	3081

prune280.0ms

Filtered

255 candidates to 79 candidates (31.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	255	2	257

Merged error: 0.0b

Counts

257 → 2

regimes32.0ms

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

sample2.0s

Algorithm

intervals

Results

817.0ms	1894×	body	10240	exit
446.0ms	7984×	body	80	valid
380.0ms	10096×	body	80	nan
9.0ms	3×	body	5120	valid
4.0ms	3×	body	2560	valid
1.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	1280	valid
0.0ms	3×	body	160	valid