Details

analyze335.0ms (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

Compiler

Compiled 24 to 18 computations (25% saved)

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 49 to 37 computations (24.5% 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

prune5.0ms (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

0.2b

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)))
	12.3b	(.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)))

12.3b

(*.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)

localize13.0ms (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 (PI.f64) a)
✓	0.2b	(/.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 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

series48.0ms (1.2%)

Counts

4 → 72

Calls

4 calls:

20.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
17.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
9.0ms	(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)))
4.0ms	(/.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))

simplify208.0ms (5.2%)

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	5404
1	676	4819
2	2133	4749
3	4629	4748
4	4989	4748
5	4998	4748
6	4972	4748

prune277.0ms (7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	229	8	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	231	8	239

Error

Counts

239 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (PI.f64) (cbrt.f64 a)))) (-.f64 b a)))
	16.3b	(.f64 (.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 (.f64 b b) (.f64 a a)))) (+.f64 b a))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
▶	0.2b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
	12.2b	(/.f64 (.f64 1/2 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (-.f64 (.f64 b b) (*.f64 a a)))
	0.7b	(.f64 (.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (/.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (-.f64 b a)))
	12.3b	(.f64 (/.f64 1/2 (-.f64 (.f64 b b) (.f64 a a))) (.f64 (-.f64 b a) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))

Compiler

Compiled 7040 to 2691 computations (61.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 1/2 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))) (+.f64 b a))
	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
	0.2b	(/.f64 (PI.f64) a)
	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))

series19.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

19.0ms

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 30

Calls

1 calls:

8.0ms

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

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

567×	`times-frac_binary64`
544×	`associate-/l*_binary64`
318×	`associate-/r*_binary64`
307×	`associate-/l/_binary64`
301×	`fma-neg_binary64`

Counts

54 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1928
1	362	1664
2	1254	1598
3	4746	1598
4	4962	1598

prune211.0ms (5.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
	16.3b	(.f64 (.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 (.f64 b b) (.f64 a a)))) (+.f64 b a))
▶	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (+.f64 b a))
	0.6b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (PI.f64) (cbrt.f64 a)))) (-.f64 b a)))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
	0.7b	(.f64 (.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (/.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (-.f64 b a)))
	12.3b	(.f64 (/.f64 1/2 (-.f64 (.f64 b b) (.f64 a a))) (.f64 (-.f64 b a) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))

Compiler

Compiled 5059 to 2047 computations (59.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series39.0ms (1%)

Counts

3 → 48

Calls

3 calls:

19.0ms	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (+.f64 b a))
17.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))
2.0ms	(/.f64 (PI.f64) b)

rewrite62.0ms (1.6%)

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:

21.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))
18.0ms	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (+.f64 b a))
2.0ms	(/.f64 (PI.f64) b)

simplify132.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

664×	`times-frac_binary64`
315×	`fma-def_binary64`
291×	`distribute-rgt-in_binary64`
265×	`distribute-lft-in_binary64`
145×	`sub-neg_binary64`

Counts

204 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	5679
1	806	5327
2	2242	5258
3	5021	5258

prune221.0ms (5.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	231	3	234
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	234	7	241

Error

Counts

241 → 7

Alt Table

Status	Error	Program
	0.5b	(/.f64 1/2 (/.f64 (+.f64 b a) (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))))
	0.7b	(/.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 (PI.f64) a) (.f64 b (PI.f64))) (.f64 (-.f64 a b) (*.f64 b a)))) (+.f64 b a))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (+.f64 b a))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
▶	0.3b	(.f64 (.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (/.f64 1 (+.f64 b a)))
	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
	0.7b	(.f64 (.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (/.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (-.f64 b a)))

Compiler

Compiled 6544 to 1867 computations (71.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (PI.f64) a)
	0.2b	(/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))
✓	0.2b	(.f64 (.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (/.f64 1 (+.f64 b a)))
	0.3b	(/.f64 (PI.f64) b)

series17.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

17.0ms

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

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
20×	`prod-exp_binary64`
18×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64`

Counts

1 → 53

Calls

1 calls:

26.0ms

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

simplify71.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-*l/_binary64`
467×	`associate-/l*_binary64`
349×	`times-frac_binary64`
242×	`associate-/r*_binary64`
240×	`fma-def_binary64`

Counts

77 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2665
1	426	2241
2	1443	2175
3	5212	2175

prune260.0ms (6.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	258	7	265

Error

Counts

265 → 7

Alt Table

Status	Error	Program
	0.5b	(/.f64 1/2 (/.f64 (+.f64 b a) (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))))
	0.7b	(/.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 (PI.f64) a) (.f64 b (PI.f64))) (.f64 (-.f64 a b) (*.f64 b a)))) (+.f64 b a))
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (+.f64 b a))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
✓	0.3b	(.f64 (.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) b) (/.f64 (PI.f64) a)) (-.f64 a b))) (/.f64 1 (+.f64 b a)))
	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
	0.7b	(.f64 (.f64 (/.f64 1/2 (+.f64 a b)) (*.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (/.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (-.f64 b a)))

Compiler

Compiled 7577 to 2472 computations (67.4% saved)

regimes839.0ms (21.1%)

Accuracy

Total 0.2b remaining (91.3%)

Threshold costs 0.2b (91.3%)

Counts

243 → 1

Compiler

Compiled 19207 to 11829 computations (38.4% 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

end1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

sample975.0ms (24.5%)

Algorithm

1×

intervals

Results

617.0ms	8000×	body	128	valid
24.0ms	353×	body	128	invalid

Compiler

Compiled 204 to 130 computations (36.3% saved)

Details

analyze335.0ms (8.4%)

sample29.0ms (0.7%)

simplify36.0ms (0.9%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series48.0ms (1.2%)

rewrite34.0ms (0.8%)

simplify208.0ms (5.2%)

prune277.0ms (7%)

localize11.0ms (0.3%)

series19.0ms (0.5%)

rewrite11.0ms (0.3%)

simplify73.0ms (1.8%)

prune211.0ms (5.3%)

localize10.0ms (0.2%)

series39.0ms (1%)

rewrite62.0ms (1.6%)

simplify132.0ms (3.3%)

prune221.0ms (5.5%)

localize11.0ms (0.3%)

series17.0ms (0.4%)

rewrite32.0ms (0.8%)

simplify71.0ms (1.8%)

prune260.0ms (6.5%)

regimes839.0ms (21.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample975.0ms (24.5%)

Profiling