Details

analyze214.0ms

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

sample22.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	12×	body	80	invalid

simplify18.0ms

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: 16.3b

Counts

2 → 1

localize15.0ms

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))))
0.5b	(/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))
3.9b	(-.f64 (.f64 b b) (.f64 a a))
11.6b	(.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)))

rewrite56.0ms

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))
25.0ms	(.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)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(.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))
17.0ms	(.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

prune204.0ms

Filtered

119 candidates to 162 candidates (-36.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	153	9	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	9	163

Merged error: 11.4b

Counts

163 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1.0 (-.f64 b a))
0.2b	(*.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a)))
0.2b	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
11.6b	(.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)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac_binary64`
193×	`*-un-lft-identity_binary64`
164×	`add-sqr-sqrt_binary64`
117×	`add-cube-cbrt_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
59×	`associate-l_binary64`
33×	`associate-r_binary64`
27×	`distribute-lft-out_binary64`
22×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`associate-/l*_binary64`
15×	`div-inv_binary64`
14×	`frac-times_binary64`
12×	`distribute-lft-out--_binary64`
11×	`pow1_binary64` `difference-of-squares_binary64`
9×	`associate-/r*_binary64`
8×	`associate-r/_binary64` `associate-/r/_binary64` `associate-l/_binary64`
6×	`flip3--_binary64` `unswap-sqr_binary64` `flip--_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 286

Calls

4 calls:

6.0ms	(/.f64 1.0 (-.f64 b a))
33.0ms	(*.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))
34.0ms	(.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)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 1.0 (-.f64 b a))
12.0ms	(*.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))
18.0ms	(.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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6239	4466

prune353.0ms

Filtered

204 candidates to 298 candidates (-46.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	290	8	298
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	295	12	307

Merged error: 0.0b

Counts

307 → 12

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac_binary64`
108×	`*-un-lft-identity_binary64`
88×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
43×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `associate-/l_binary64` `div-exp_binary64` `associate-l/_binary64`
12×	`associate-l_binary64` `distribute-lft-out--_binary64`
11×	`div-inv_binary64`
10×	`difference-of-squares_binary64`
9×	`associate-/r*_binary64` `pow1_binary64`
8×	`associate-/l/_binary64`
6×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `frac-times_binary64`
5×	`frac-sub_binary64`
4×	`associate-/r/_binary64`
3×	`pow-prod-down_binary64`
2×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 185

Calls

4 calls:

13.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
31.0ms	(/.f64 (.f64 (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)) (.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) 1.0)) (-.f64 b a))
11.0ms	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
26.0ms	(.f64 (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)) (.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) 1.0))

series53.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
17.0ms	(/.f64 (.f64 (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)) (.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) 1.0)) (-.f64 b a))
12.0ms	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
18.0ms	(.f64 (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)) (.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) 1.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4988	3060
1	4988	3060

prune244.0ms

Filtered

141 candidates to 197 candidates (-39.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	193	4	197
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	197	12	209

Merged error: 0.0b

Counts

209 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

226×	`times-frac_binary64`
193×	`*-un-lft-identity_binary64`
148×	`add-sqr-sqrt_binary64`
117×	`add-cube-cbrt_binary64`
79×	`associate-l_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`distribute-lft-out_binary64`
17×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
16×	`associate-r/_binary64` `associate-/l_binary64` `frac-times_binary64`
15×	`div-inv_binary64`
13×	`associate-r_binary64`
12×	`distribute-lft-out--_binary64`
11×	`pow1_binary64` `difference-of-squares_binary64`
9×	`associate-/r*_binary64`
8×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
6×	`sub-neg_binary64` `frac-sub_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-*l/_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 286

Calls

4 calls:

6.0ms	(/.f64 1.0 (-.f64 b a))
37.0ms	(.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b))))
9.0ms	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
25.0ms	(*.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 1.0 (-.f64 b a))
17.0ms	(.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b))))
9.0ms	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))
10.0ms	(*.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))

simplify69.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	6239	4864

prune323.0ms

Filtered

208 candidates to 298 candidates (-43.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	295	3	298
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	299	11	310

Merged error: 0b

Counts

310 → 11

regimes126.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	13
1	14	13

end0.0ms

sample611.0ms

Algorithm

intervals

Results

452.0ms	8000×	body	80	valid
21.0ms	386×	body	80	invalid

Details

analyze214.0ms

sample22.0ms

simplify18.0ms

prune3.0ms

localize15.0ms

rewrite56.0ms

series47.0ms

simplify53.0ms

prune204.0ms

localize12.0ms

rewrite100.0ms

series46.0ms

simplify66.0ms

prune353.0ms

localize12.0ms

rewrite90.0ms

series53.0ms

simplify60.0ms

prune244.0ms

localize13.0ms

rewrite92.0ms

series43.0ms

simplify69.0ms

prune323.0ms

regimes126.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample611.0ms

Profiling