Details

analyze248.0ms

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

sample37.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
1.0ms	7×	body	80	invalid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5043	18

prune6.0ms

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

localize14.0ms

Local error

Found 4 expressions with local error:

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

31.0ms	(/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a))
48.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.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)

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5347	3397

prune158.0ms

Filtered

169 candidates to 256 candidates (-51.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	245	11	256
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	247	11	258

Merged error: 0b

Counts

258 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a))) (+.f64 b a))
0.2b	(/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a))
0.3b	(/.f64 PI.f64 a)
0.3b	(/.f64 PI.f64 b)

rewrite61.0ms

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` `associate-*r/_binary64` `div-sub_binary64` `flip-+_binary64` `frac-sub_binary64`

Counts

4 → 177

Calls

4 calls:

25.0ms	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a))) (+.f64 b a))
19.0ms	(/.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)

series24.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify52.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5822	2746

prune87.0ms

Filtered

134 candidates to 189 candidates (-41.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	192	8	200

Merged error: 0b

Counts

200 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.1b	(/.f64 (.f64 1/2 (.f64 PI.f64 (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
0.2b	(/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a))
0.3b	(*.f64 PI.f64 (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

453×	`add-sqr-sqrt_binary64`
411×	`times-frac_binary64`
356×	`*-un-lft-identity_binary64`
147×	`difference-of-squares_binary64`
123×	`distribute-lft-out--_binary64`
101×	`associate-r_binary64`
82×	`add-cube-cbrt_binary64`
51×	`div-inv_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`associate-/l*_binary64`
9×	`associate-/r*_binary64`
7×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64`
4×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
3×	`associate-r/_binary64` `associate-l*_binary64`
2×	`distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 315

Calls

4 calls:

14.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
34.0ms	(/.f64 (.f64 1/2 (.f64 PI.f64 (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
22.0ms	(/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a))
41.0ms	(*.f64 PI.f64 (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
17.0ms	(/.f64 (.f64 1/2 (.f64 PI.f64 (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
5.0ms	(/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a))
7.0ms	(*.f64 PI.f64 (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

327 → 327

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5222	5225

prune184.0ms

Filtered

178 candidates to 327 candidates (-83.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	327	0	327
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	327	8	335

Merged error: 0b

Counts

335 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 1/2 (/.f64 PI.f64 (.f64 b a)))
0.1b	(/.f64 (.f64 1/2 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
1.1b	(/.f64 PI.f64 (*.f64 b a))

rewrite25.0ms

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 1/2 (/.f64 PI.f64 (.f64 b a)))
10.0ms	(/.f64 (.f64 1/2 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
5.0ms	(/.f64 PI.f64 (*.f64 b a))

series19.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(.f64 1/2 (/.f64 PI.f64 (.f64 b a)))
10.0ms	(/.f64 (.f64 1/2 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
4.0ms	(/.f64 PI.f64 (*.f64 b a))

simplify38.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4983	759
1	4983	759

prune39.0ms

Filtered

56 candidates to 87 candidates (-55.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	89	6	95

Merged error: 0b

Counts

95 → 6

regimes64.0ms

Accuracy

0% (0.3b 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	50	19
1	50	19

end0.0ms

sample618.0ms

Algorithm

intervals

Results

452.0ms	8000×	body	80	valid
22.0ms	367×	body	80	invalid

Details

analyze248.0ms

sample37.0ms

simplify49.0ms

prune6.0ms

localize14.0ms

rewrite100.0ms

series25.0ms

simplify61.0ms

prune158.0ms

localize10.0ms

rewrite61.0ms

series24.0ms

simplify52.0ms

prune87.0ms

localize11.0ms

rewrite134.0ms

series32.0ms

simplify54.0ms

prune184.0ms

localize7.0ms

rewrite25.0ms

series19.0ms

simplify38.0ms

prune39.0ms

regimes64.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample618.0ms

Profiling