Details

analyze216.0ms

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

sample30.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
1.0ms	13×	body	80	invalid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5043	18

prune17.0ms

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: 0.2b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

266×	`*-un-lft-identity_binary64`
223×	`times-frac_binary64`
140×	`add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
58×	`distribute-lft-out_binary64`
46×	`associate-r_binary64`
45×	`distribute-rgt-neg-in_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`associate-/l*_binary64`
18×	`associate-l_binary64`
17×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
12×	`distribute-lft-neg-in_binary64`
11×	`associate-/r*_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64` `associate-/r/_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `neg-mul-1_binary64` `unswap-sqr_binary64` `div-sub_binary64` `prod-exp_binary64`
3×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `neg-sub0_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `associate-r/_binary64` `frac-add_binary64` `frac-times_binary64` `unsub-neg_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 244

Calls

4 calls:

46.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a)))
30.0ms	(/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a))
3.0ms	(/.f64 PI.f64 a)
5.0ms	(/.f64 (neg.f64 PI.f64) b)

series27.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a)))
7.0ms	(/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a))
3.0ms	(/.f64 PI.f64 a)
3.0ms	(/.f64 (neg.f64 PI.f64) b)

simplify62.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5347	3397

prune249.0ms

Filtered

169 candidates to 256 candidates (-51.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	247	9	256
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	248	10	258

Merged error: 0b

Counts

258 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-sqr-sqrt_binary64`
142×	`times-frac_binary64`
131×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`
43×	`distribute-lft-out--_binary64`
37×	`difference-of-squares_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
16×	`div-inv_binary64`
15×	`associate-/r*_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `div-sub_binary64` `flip-+_binary64` `frac-sub_binary64` `associate-*l/_binary64`

Counts

4 → 177

Calls

4 calls:

25.0ms	(/.f64 (*.f64 (/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a)) 1/2) (+.f64 b a))
18.0ms	(/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a))
3.0ms	(/.f64 PI.f64 a)
3.0ms	(/.f64 PI.f64 b)

series27.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/.f64 (*.f64 (/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a)) 1/2) (+.f64 b a))
7.0ms	(/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a))
2.0ms	(/.f64 PI.f64 a)
3.0ms	(/.f64 PI.f64 b)

simplify53.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	6213	2735

prune197.0ms

Filtered

132 candidates to 189 candidates (-43.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	189	10	199

Merged error: 0b

Counts

199 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
44×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`associate-/r*_binary64`
11×	`distribute-lft-out--_binary64`
10×	`div-inv_binary64`
8×	`associate-/l*_binary64` `div-exp_binary64`
7×	`cbrt-undiv_binary64`
6×	`pow1_binary64` `prod-exp_binary64`
5×	`associate-/l/_binary64` `difference-of-squares_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `un-div-inv_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `1-exp_binary64` `div-sub_binary64` `rec-exp_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 139

Calls

4 calls:

18.0ms	(/.f64 (.f64 (/.f64 (-.f64 (/.f64 PI.f64 a) (.f64 PI.f64 (/.f64 1 b))) (-.f64 b a)) 1/2) (+.f64 b a))
11.0ms	(/.f64 (-.f64 (/.f64 PI.f64 a) (*.f64 PI.f64 (/.f64 1 b))) (-.f64 b a))
3.0ms	(/.f64 PI.f64 a)
8.0ms	(*.f64 PI.f64 (/.f64 1 b))

series24.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (.f64 (/.f64 (-.f64 (/.f64 PI.f64 a) (.f64 PI.f64 (/.f64 1 b))) (-.f64 b a)) 1/2) (+.f64 b a))
7.0ms	(/.f64 (-.f64 (/.f64 PI.f64 a) (*.f64 PI.f64 (/.f64 1 b))) (-.f64 b a))
2.0ms	(/.f64 PI.f64 a)
3.0ms	(*.f64 PI.f64 (/.f64 1 b))

simplify60.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	6032	1689

prune135.0ms

Filtered

104 candidates to 151 candidates (-45.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	151	10	161

Merged error: 0b

Counts

161 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1/2 (+.f64 b a))
0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 PI.f64 (.f64 b a)))
0.9b	(/.f64 PI.f64 (*.f64 b a))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
31×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
18×	`associate-l_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`distribute-lft-out_binary64` `associate-r_binary64`
6×	`associate-/l*_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`associate-/r/_binary64` `div-inv_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 105

Calls

3 calls:

5.0ms	(/.f64 1/2 (+.f64 b a))
13.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 PI.f64 (.f64 b a)))
4.0ms	(/.f64 PI.f64 (*.f64 b a))

series18.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/.f64 1/2 (+.f64 b a))
9.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 PI.f64 (.f64 b a)))
4.0ms	(/.f64 PI.f64 (*.f64 b a))

simplify65.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4974	1064
1	4974	1064

prune121.0ms

Filtered

77 candidates to 114 candidates (-48.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	5	2	7
Picked	0	1	1
Done	1	1	2
Total	117	7	124

Merged error: 0b

Counts

124 → 7

regimes96.0ms

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	39	17
1	39	17

end0.0ms

sample640.0ms

Algorithm

intervals

Results

476.0ms	8000×	body	80	valid
26.0ms	409×	body	80	invalid

Details

analyze216.0ms

sample30.0ms

simplify73.0ms

prune17.0ms

localize12.0ms

rewrite100.0ms

series27.0ms

simplify62.0ms

prune249.0ms

localize12.0ms

rewrite58.0ms

series27.0ms

simplify53.0ms

prune197.0ms

localize11.0ms

rewrite44.0ms

series24.0ms

simplify60.0ms

prune135.0ms

localize7.0ms

rewrite26.0ms

series18.0ms

simplify65.0ms

prune121.0ms

regimes96.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample640.0ms

Profiling