Details

analyze215.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

sample24.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
1.0ms	10×	body	80	invalid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5006	29

prune4.0ms

Filtered

1 candidates to 1 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: 13.3b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
1.4b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.8b	(-.f64 (.f64 b b) (.f64 a a))
6.6b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

224×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
132×	`*-un-lft-identity_binary64`
100×	`add-cube-cbrt_binary64`
58×	`associate-l_binary64`
46×	`difference-of-squares_binary64`
19×	`associate-r_binary64` `div-inv_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
4×	`associate-/r*_binary64` `sub-neg_binary64` `associate-/r/_binary64`
3×	`cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-sub_binary64` `frac-times_binary64`
2×	`diff-log_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 230

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))
44.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
35.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
26.0ms	(-.f64 (.f64 b b) (.f64 a a))
46.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

simplify101.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5171	6697

prune279.0ms

Filtered

194 candidates to 242 candidates (-24.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	234	8	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	236	8	244

Merged error: 0.0b

Counts

244 → 8

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
60×	`add-exp-log_binary64`
51×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
39×	`add-cbrt-cube_binary64`
29×	`div-exp_binary64`
19×	`prod-exp_binary64`
17×	`cbrt-undiv_binary64`
14×	`distribute-lft-out_binary64` `associate-/l*_binary64`
10×	`cbrt-unprod_binary64`
7×	`div-inv_binary64`
6×	`1-exp_binary64`
5×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

2 → 122

Calls

2 calls:

16.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
8.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series92.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
50.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify77.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5151	2615

prune96.0ms

Filtered

78 candidates to 128 candidates (-64.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	126	10	136

Merged error: 0b

Counts

136 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (-.f64 b a))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
0.3b	(/.f64 PI.f64 (+.f64 b a))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity_binary64`
86×	`add-sqr-sqrt_binary64`
73×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
37×	`associate-l_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`associate-r_binary64`
16×	`difference-of-squares_binary64` `frac-times_binary64`
14×	`distribute-lft-out--_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
10×	`associate-r/_binary64` `associate-l/_binary64`
9×	`associate-/r*_binary64`
8×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-/l*_binary64` `frac-sub_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 188

Calls

4 calls:

5.0ms	(/.f64 1/2 (-.f64 b a))
29.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
5.0ms	(/.f64 PI.f64 (+.f64 b a))
26.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 1/2 (-.f64 b a))
45.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
22.0ms	(/.f64 PI.f64 (+.f64 b a))
26.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5022	4131

prune172.0ms

Filtered

143 candidates to 200 candidates (-39.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	201	9	210

Merged error: 0b

Counts

210 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) 1/2) (-.f64 b a)))
0.3b	(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) 1/2) (-.f64 b a))
0.3b	(/.f64 PI.f64 (+.f64 b a))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
53×	`times-frac_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`add-cube-cbrt_binary64`
18×	`associate-l_binary64`
12×	`difference-of-squares_binary64`
11×	`associate-r_binary64`
10×	`cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
9×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
8×	`associate-/r/_binary64` `div-inv_binary64`
7×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`flip3--_binary64` `associate-/l_binary64` `flip--_binary64` `associate-l/_binary64`
3×	`associate-/l/_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 146

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
29.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) 1/2) (-.f64 b a)))
19.0ms	(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) 1/2) (-.f64 b a))
5.0ms	(/.f64 PI.f64 (+.f64 b a))

series113.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
50.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) 1/2) (-.f64 b a)))
26.0ms	(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) 1/2) (-.f64 b a))
26.0ms	(/.f64 PI.f64 (+.f64 b a))

simplify85.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5010	3416

prune105.0ms

Filtered

105 candidates to 158 candidates (-50.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	158	9	167

Merged error: 0b

Counts

167 → 9

regimes38.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	17
1	17	17

end0.0ms

sample637.0ms

Algorithm

intervals

Results

464.0ms	8000×	body	80	valid
19.0ms	335×	body	80	invalid

Details

analyze215.0ms

sample24.0ms

simplify67.0ms

prune4.0ms

localize12.0ms

rewrite82.0ms

series116.0ms

simplify101.0ms

prune279.0ms

localize8.0ms

rewrite30.0ms

series92.0ms

simplify77.0ms

prune96.0ms

localize12.0ms

rewrite73.0ms

series116.0ms

simplify77.0ms

prune172.0ms

localize12.0ms

rewrite72.0ms

series113.0ms

simplify85.0ms

prune105.0ms

regimes38.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample637.0ms

Profiling