Details

analyze193.0ms (4.8%)

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
12.5%	87.4%	0.1%	5
25%	74.9%	0.1%	6
46.8%	53.1%	0.1%	7
56.2%	43.7%	0.1%	8
71%	28.9%	0.1%	9
76.5%	23.4%	0.1%	10
84.9%	15%	0.1%	11
87.8%	12.1%	0.1%	12
92.2%	7.7%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample963.0ms (23.9%)

Infinites

16.9% of outputs are infinite.

Results

879.0ms

8256×

body

128

valid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify36.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

693×	`div-sub_binary64`
599×	`times-frac_binary64`
519×	`associate-/l*_binary64`
357×	`associate-/l/_binary64`
274×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	37	29
2	94	29
3	345	29
4	1207	28
5	3468	28
6	5020	28

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	13.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Status

Error

Program

▶

0.2b

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

13.6b

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

Compiler

Compiled 127 to 87 computations (31.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
✓	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
✓	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
✓	0.2b	(/.f64 (PI.f64) a)

series46.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

18.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
18.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
8.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
2.0ms	(/.f64 (PI.f64) a)

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
55×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

4 → 143

Calls

4 calls:

14.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
5.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
2.0ms	(/.f64 (PI.f64) a)
0.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))

simplify195.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

425×	`times-frac_binary64`
380×	`associate-/l/_binary64`
318×	`fma-neg_binary64`
291×	`fma-def_binary64`
232×	`distribute-rgt-in_binary64`

Counts

215 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	5398
1	676	4819
2	2133	4749
3	4629	4748
4	4989	4748
5	4998	4748
6	4972	4748

prune228.0ms (5.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

Counts

239 → 7

Alt Table

Status	Error	Program
	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))))
	0.2b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	34.5b	(.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (sqrt.f64 (-.f64 b a)))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (sqrt.f64 (-.f64 b a))))
▶	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	5.3b	(.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a))))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (cbrt.f64 (-.f64 b a))))
	13.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))

Compiler

Compiled 6954 to 2637 computations (62.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
	0.2b	(/.f64 (PI.f64) a)
✓	0.3b	(/.f64 (PI.f64) b)

series37.0ms (0.9%)

Counts

3 → 48

Calls

3 calls:

17.0ms	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
17.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
2.0ms	(/.f64 (PI.f64) b)

rewrite59.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`add-sqr-sqrt_binary64`
133×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
43×	`distribute-lft-out--_binary64`

Counts

3 → 156

Calls

3 calls:

19.0ms	(/.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))
2.0ms	(/.f64 (PI.f64) b)

simplify151.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

663×	`times-frac_binary64`
311×	`fma-def_binary64`
299×	`fma-neg_binary64`
273×	`distribute-rgt-in_binary64`
248×	`distribute-lft-in_binary64`

Counts

204 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	5679
1	798	5327
2	2228	5259
3	4971	5259
4	5149	5259

prune188.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	238	6	244

Error

Counts

244 → 6

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
	0.2b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	5.3b	(.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a))))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (cbrt.f64 (-.f64 b a))))
	13.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 6643 to 1844 computations (72.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
✓	0.1b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
✓	0.5b	(/.f64 (PI.f64) (*.f64 a b))

series39.0ms (1%)

Counts

3 → 24

Calls

3 calls:

17.0ms	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
12.0ms	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
10.0ms	(/.f64 (PI.f64) (*.f64 a b))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 84

Calls

3 calls:

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

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

860×	`associate-/r*_binary64`
606×	`associate-/l/_binary64`
435×	`associate-/r/_binary64`
248×	`fma-def_binary64`
140×	`cancel-sign-sub-inv_binary64`

Counts

108 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2343
1	474	2001
2	1614	1934
3	4969	1934

prune112.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	125	6	131

Error

Counts

131 → 6

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
	0.2b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
▶	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	5.3b	(.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a))))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (cbrt.f64 (-.f64 b a))))
	13.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 2482 to 1029 computations (58.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))
	0.2b	(/.f64 (PI.f64) a)
	0.3b	(/.f64 (PI.f64) b)
✓	0.4b	(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))

series44.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))
17.0ms	(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))

rewrite114.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

761×	`times-frac_binary64`
647×	`add-sqr-sqrt_binary64`
543×	`*-un-lft-identity_binary64`
213×	`add-cube-cbrt_binary64`
191×	`distribute-lft-out--_binary64`

Counts

2 → 391

Calls

2 calls:

20.0ms	(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))
13.0ms	(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))

simplify348.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
419×	`associate-/r/_binary64`
369×	`times-frac_binary64`
325×	`associate-/r*_binary64`
317×	`distribute-rgt-in_binary64`

Counts

439 → 437

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	14610
1	667	13806
2	2036	13407
3	4565	13407
4	5148	13407

prune422.0ms (10.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	500	0	500
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	500	6	506

Error

Counts

506 → 6

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
	0.2b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
✓	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	5.3b	(.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a))))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (cbrt.f64 (-.f64 b a))))
	13.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

Compiler

Compiled 16877 to 4694 computations (72.2% saved)

regimes605.0ms (15%)

Accuracy

Total 0.2b remaining (81.2%)

Threshold costs 0.2b (81.2%)

Counts

160 → 1

Compiler

Compiled 11359 to 7182 computations (36.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
1	19	27
2	29	27
3	35	27
4	39	27
5	40	27
6	40	27

end93.0ms (2.3%)

Compiler: Compiled 167 to 107 computations (35.9% saved)

Details

analyze193.0ms (4.8%)

sample963.0ms (23.9%)

simplify36.0ms (0.9%)

prune4.0ms (0.1%)

localize12.0ms (0.3%)

series46.0ms (1.1%)

rewrite34.0ms (0.8%)

simplify195.0ms (4.8%)

prune228.0ms (5.7%)

localize10.0ms (0.3%)

series37.0ms (0.9%)

rewrite59.0ms (1.5%)

simplify151.0ms (3.8%)

prune188.0ms (4.7%)

localize7.0ms (0.2%)

series39.0ms (1%)

rewrite20.0ms (0.5%)

simplify59.0ms (1.5%)

prune112.0ms (2.8%)

localize11.0ms (0.3%)

series44.0ms (1.1%)

rewrite114.0ms (2.8%)

simplify348.0ms (8.6%)

prune422.0ms (10.5%)

regimes605.0ms (15%)

simplify3.0ms (0.1%)

end93.0ms (2.3%)

Profiling