Details

analyze222.0ms

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

sample21.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	7×	body	80	invalid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5167	21

prune3.0ms

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: 14.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 PI.f64 2.0) (/.f64 1.0 (-.f64 (.f64 b b) (*.f64 a a))))
0.6b	(/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))
3.6b	(-.f64 (.f64 b b) (.f64 a a))
10.3b	(.f64 (.f64 (/.f64 PI.f64 2.0) (/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
47×	`times-frac_binary64`
39×	`*-un-lft-identity_binary64`
36×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
31×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`
14×	`associate-l_binary64` `frac-times_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`difference-of-squares_binary64`
11×	`pow1_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`associate-r/_binary64` `associate-l/_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64`
5×	`distribute-lft-out--_binary64` `div-inv_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `frac-sub_binary64`
3×	`sub-neg_binary64` `associate-/l*_binary64`
2×	`*-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 150

Calls

4 calls:

15.0ms	(.f64 (/.f64 PI.f64 2.0) (/.f64 1.0 (-.f64 (.f64 b b) (*.f64 a a))))
6.0ms	(/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))
24.0ms	(.f64 (.f64 (/.f64 PI.f64 2.0) (/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (/.f64 PI.f64 2.0) (/.f64 1.0 (-.f64 (.f64 b b) (*.f64 a a))))
11.0ms	(/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))
7.0ms	(-.f64 (.f64 b b) (.f64 a a))
15.0ms	(.f64 (.f64 (/.f64 PI.f64 2.0) (/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5018	2608

prune193.0ms

Filtered

119 candidates to 162 candidates (-36.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	10	163

Merged error: 10.2b

Counts

163 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
0.2b	(*.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a)))
0.3b	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
10.3b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a))) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac_binary64`
185×	`*-un-lft-identity_binary64`
160×	`add-sqr-sqrt_binary64`
109×	`add-cube-cbrt_binary64`
59×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
33×	`associate-r_binary64`
27×	`distribute-lft-out_binary64`
21×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`div-inv_binary64`
14×	`frac-times_binary64`
13×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
11×	`pow1_binary64` `difference-of-squares_binary64`
8×	`associate-r/_binary64` `associate-l/_binary64`
6×	`add-log-exp_binary64` `flip3--_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip--_binary64`
5×	`frac-sub_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64`
3×	`sub-neg_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 270

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
32.0ms	(*.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a)))
8.0ms	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
32.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a))) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
11.0ms	(*.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a)))
9.0ms	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
15.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a))) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

simplify64.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	6226	4402

prune323.0ms

Filtered

194 candidates to 282 candidates (-45.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	275	7	282
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	283	9	292

Merged error: 0.0b

Counts

292 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
0.2b	(/.f64 (.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))) (+.f64 b a))
0.3b	(.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b))))
0.3b	(*.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
59×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
53×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
34×	`associate-l_binary64`
29×	`associate-*r/_binary64` `frac-times_binary64`
27×	`add-cube-cbrt_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64`
18×	`cbrt-undiv_binary64` `div-exp_binary64`
15×	`associate-/l/_binary64`
13×	`associate-r_binary64` `distribute-lft-out--_binary64`
12×	`flip3--_binary64` `flip--_binary64`
11×	`pow1_binary64` `difference-of-squares_binary64` `frac-sub_binary64`
7×	`sub-neg_binary64` `div-inv_binary64` `associate-*l/_binary64`
6×	`add-log-exp_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64` `associate-/r/_binary64`
2×	`distribute-lft-out_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `flip-+_binary64`

Counts

4 → 183

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
32.0ms	(/.f64 (.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))) (+.f64 b a))
25.0ms	(.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b))))
25.0ms	(*.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
15.0ms	(/.f64 (.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))) (+.f64 b a))
11.0ms	(.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b))))
9.0ms	(*.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

simplify59.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5003	3272

prune218.0ms

Filtered

138 candidates to 195 candidates (-41.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	191	4	195
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	194	10	204

Merged error: 0.0b

Counts

204 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 0.5 (/.f64 PI.f64 (.f64 b a)))
0.2b	(/.f64 (.f64 0.5 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
0.6b	(/.f64 PI.f64 (*.f64 b a))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`cbrt-undiv_binary64` `add-cube-cbrt_binary64` `times-frac_binary64` `div-exp_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`associate-/l*_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`distribute-lft-out_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 78

Calls

3 calls:

7.0ms	(.f64 0.5 (/.f64 PI.f64 (.f64 b a)))
10.0ms	(/.f64 (.f64 0.5 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
5.0ms	(/.f64 PI.f64 (*.f64 b a))

series23.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(.f64 0.5 (/.f64 PI.f64 (.f64 b a)))
13.0ms	(/.f64 (.f64 0.5 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
4.0ms	(/.f64 PI.f64 (*.f64 b a))

simplify32.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4991	761
1	4991	761

prune66.0ms

Filtered

56 candidates to 87 candidates (-55.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	89	8	97

Merged error: 0b

Counts

97 → 8

regimes94.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

end0.0ms

sample604.0ms

Algorithm

intervals

Results

451.0ms	8000×	body	80	valid
21.0ms	349×	body	80	invalid

Details

analyze222.0ms

sample21.0ms

simplify17.0ms

prune3.0ms

localize16.0ms

rewrite54.0ms

series43.0ms

simplify53.0ms

prune193.0ms

localize12.0ms

rewrite101.0ms

series40.0ms

simplify64.0ms

prune323.0ms

localize15.0ms

rewrite102.0ms

series40.0ms

simplify59.0ms

prune218.0ms

localize7.0ms

rewrite23.0ms

series23.0ms

simplify32.0ms

prune66.0ms

regimes94.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample604.0ms

Profiling