Details

sample65.0ms

Algorithm

intervals

Results

24.0ms	57×	body	10240	exit
14.0ms	256×	body	80	valid
12.0ms	336×	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

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

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))
1.0ms	(sqrt (atan2 b b))

series89.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sqrt (atan2 b b))

simplify75.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (68.0ms)

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

prune126.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:

21.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
3.0ms	(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))

series146.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
87.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
9.0ms	(sqrt (atan2 b b))
13.0ms	(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

prune346.0ms

Filtered

183 candidates to 96 candidates (52.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	182	5	187

Merged error: 0.0b

Counts

187 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0b	(pow (atan2 b b) (* 1/2 (- b a)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
18×	`prod-diff`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`distribute-rgt-in` `distribute-lft-in`
3×	`pow1` `add-exp-log` `unpow-prod-down`
2×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 48

Calls

2 calls:

5.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
5.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series80.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
20.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify100.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	324	582
1	913	448
2	3678	428
3	5001	425

prune77.0ms

Filtered

54 candidates to 27 candidates (50.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Merged error: 0.0b

Counts

59 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (atan2 b b) (- b a)) 3/2)
0.0b	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))
0.0b	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
0.0b	(pow (atan2 b b) (- b a))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

45×	`unpow-prod-down`
33×	`unpow-prod-up`
32×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
27×	`prod-diff`
22×	`cbrt-prod`
8×	`pow-unpow`
7×	`add-exp-log`
5×	`pow1` `pow-exp` `sqr-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `sub-neg`
2×	`pow-pow`
1×	`pow1/3` `distribute-lft-out--` `pow-sub` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

9.0ms	(pow (pow (atan2 b b) (- b a)) 3/2)
6.0ms	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))
7.0ms	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
5.0ms	(pow (atan2 b b) (- b a))

series154.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (pow (atan2 b b) (- b a)) 3/2)
27.0ms	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))
71.0ms	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
17.0ms	(pow (atan2 b b) (- b a))

simplify44.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	420	1161
1	1181	957
2	5001	938

prune236.0ms

Filtered

122 candidates to 77 candidates (63.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	123	3	126

Merged error: 0.0b

Counts

126 → 3

regimes35.0ms

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	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

798.0ms	1790×	body	10240	exit
440.0ms	7992×	body	80	valid
359.0ms	9874×	body	80	nan
6.0ms	2×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid