Details

sample58.0ms

Algorithm

intervals

Results

19.0ms	52×	body	10240	exit
14.0ms	256×	body	80	valid
11.0ms	308×	body	80	nan

simplify53.0ms

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: 0.0b

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))

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:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

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

prune101.0ms

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	(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))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
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×	`pow1/2` `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 → 162

Calls

4 calls:

6.0ms	(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))

series89.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify55.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	292	1754
1	1319	1646
2	5002	1602

prune284.0ms

Filtered

174 candidates to 84 candidates (48.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	173	3	176

Merged error: 0.0b

Counts

176 → 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))

rewrite14.0ms

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:

5.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sqrt (atan2 b b))

series115.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
29.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify147.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	217	461
1	743	419
2	3883	391
3	5002	369

prune104.0ms

Filtered

59 candidates to 34 candidates (57.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	60	2	62

Merged error: 0.0b

Counts

62 → 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))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

79×	`unpow-prod-down`
48×	`sqrt-prod`
40×	`cbrt-prod`
34×	`cube-prod`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
20×	`unpow-prod-up`
10×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
8×	`pow1`
7×	`add-exp-log` `sqr-pow`
6×	`pow-pow`
5×	`sqrt-pow1` `pow-exp` `add-cbrt-cube`
4×	`pow-unpow` `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 → 145

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
7.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
8.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3))
2.0ms	(sqrt (atan2 b b))

series126.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
54.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
29.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3))
11.0ms	(sqrt (atan2 b b))

simplify59.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	390	1632
1	1533	1551
2	5001	1504

prune227.0ms

Filtered

157 candidates to 65 candidates (41.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	157	2	159

Merged error: 0.0b

Counts

159 → 2

regimes31.0ms

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

832.0ms	1894×	body	10240	exit
449.0ms	7984×	body	80	valid
362.0ms	10096×	body	80	nan
9.0ms	3×	body	5120	valid
3.0ms	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