Details

analyze238.0ms (8.4%)

Algorithm

1×

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 (0.8%)

Algorithm

1×

intervals

Results

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

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5167	21

prune5.0ms (0.2%)

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

localize14.0ms (0.5%)

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)))

rewrite57.0ms (2%)

Algorithm

1×	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:

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)))
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))

series47.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(.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)))
11.0ms	(.f64 (/.f64 PI.f64 2.0) (/.f64 1.0 (-.f64 (.f64 b b) (*.f64 a a))))
9.0ms	(/.f64 1.0 (-.f64 (.f64 b b) (.f64 a a)))
7.0ms	(-.f64 (.f64 b b) (.f64 a a))

simplify52.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5018	2608

prune251.0ms (8.9%)

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 (0.4%)

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)))

rewrite107.0ms (3.8%)

Algorithm

1×	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:

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)))
33.0ms	(*.f64 (/.f64 (/.f64 PI.f64 2.0) (+.f64 b a)) (/.f64 1.0 (-.f64 b a)))
13.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))
9.0ms	(/.f64 (/.f64 PI.f64 2.0) (+.f64 b a))

series43.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(.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)))
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))
5.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))

simplify63.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	6226	4402

prune457.0ms (16.2%)

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

localize12.0ms (0.4%)

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)))

rewrite105.0ms (3.7%)

Algorithm

1×	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:

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))
26.0ms	(*.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))
25.0ms	(.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b))))
13.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))

series48.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(/.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))
12.0ms	(.f64 (/.f64 PI.f64 2.0) (.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b))))
10.0ms	(*.f64 (/.f64 1.0 (-.f64 b a)) (-.f64 (/.f64 1.0 a) (/.f64 1.0 b)))
9.0ms	(-.f64 (/.f64 1.0 a) (/.f64 1.0 b))

simplify60.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5003	3272

prune306.0ms (10.8%)

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

localize15.0ms (0.5%)

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))

rewrite42.0ms (1.5%)

Algorithm

1×	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:

17.0ms	(/.f64 (.f64 0.5 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
12.0ms	(.f64 0.5 (/.f64 PI.f64 (.f64 b a)))
8.0ms	(/.f64 PI.f64 (*.f64 b a))

series34.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

21.0ms	(/.f64 (.f64 0.5 (/.f64 PI.f64 (.f64 b a))) (+.f64 b a))
7.0ms	(/.f64 PI.f64 (*.f64 b a))
6.0ms	(.f64 0.5 (/.f64 PI.f64 (.f64 b a)))

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4991	761
1	4991	761

prune92.0ms (3.3%)

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

regimes97.0ms (3.4%)

Accuracy

Total 0.2b remaining (92.9%)

Threshold costs 0.2b (92.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

end0.0ms (0%)

sample596.0ms (21.1%)

Algorithm

1×

intervals

Results

441.0ms	8000×	body	80	valid
20.0ms	349×	body	80	invalid

Details

analyze238.0ms (8.4%)

sample21.0ms (0.8%)

simplify18.0ms (0.6%)

prune5.0ms (0.2%)

localize14.0ms (0.5%)

rewrite57.0ms (2%)

series47.0ms (1.7%)

simplify52.0ms (1.9%)

prune251.0ms (8.9%)

localize12.0ms (0.4%)

rewrite107.0ms (3.8%)

series43.0ms (1.5%)

simplify63.0ms (2.2%)

prune457.0ms (16.2%)

localize12.0ms (0.4%)

rewrite105.0ms (3.7%)

series48.0ms (1.7%)

simplify60.0ms (2.1%)

prune306.0ms (10.8%)

localize15.0ms (0.5%)

rewrite42.0ms (1.5%)

series34.0ms (1.2%)

simplify32.0ms (1.1%)

prune92.0ms (3.3%)

regimes97.0ms (3.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample596.0ms (21.1%)

Profiling