Details

analyze316.0ms (6.3%)

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)

sample1.3s (25.2%)

Results

1.2s	8256×	body	128	valid
46.0ms	351×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify37.0ms (0.7%)

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

prune7.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.3b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
▶	0.5b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

Status

Error

Program

14.3b

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

▶

0.5b

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

Compiler

Compiled 127 to 87 computations (31.5% saved)

localize10.0ms (0.2%)

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 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
✓	0.5b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))

series49.0ms (1%)

Counts

4 → 72

Calls

4 calls:

19.0ms	(/.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)))
11.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
2.0ms	(/.f64 (PI.f64) a)

rewrite32.0ms (0.6%)

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:

13.0ms	(*.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))

simplify219.0ms (4.3%)

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

prune242.0ms (4.8%)

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

0.0b

Counts

239 → 7

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	14.3b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	23.8b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a (*.f64 a b))))
	1.1b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (cbrt.f64 (-.f64 b a))))
	0.5b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	0.6b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	29.5b	(.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (/.f64 1/2 (+.f64 a b))) (sqrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))

Compiler

Compiled 6954 to 2636 computations (62.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (+.f64 b a))
✓	0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
✓	0.4b	(/.f64 (PI.f64) (*.f64 a b))

series42.0ms (0.8%)

Counts

3 → 48

Calls

3 calls:

18.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
13.0ms	(/.f64 1/2 (+.f64 b a))
10.0ms	(/.f64 (PI.f64) (*.f64 a b))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
29×	`add-sqr-sqrt_binary64`

Counts

3 → 111

Calls

3 calls:

9.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
4.0ms	(/.f64 1/2 (+.f64 b a))
3.0ms	(/.f64 (PI.f64) (*.f64 a b))

simplify143.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
408×	`fma-def_binary64`
359×	`associate-/l/_binary64`
205×	`cancel-sign-sub-inv_binary64`
200×	`associate-/r/_binary64`

Counts

159 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	3408
1	649	3007
2	2241	2905
3	4593	2905
4	5036	2905

prune188.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	189	5	194
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	194	7	201

Error

Counts

201 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (+.f64 a b))) (/.f64 (PI.f64) (*.f64 a b)))
▶	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (PI.f64) a) b))
	3.7b	(*.f64 (/.f64 (/.f64 1/2 a) (+.f64 a b)) (/.f64 (PI.f64) b))
✓	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.8b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	17.9b	(.f64 (sqrt.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))) (sqrt.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (*.f64 a b)))))
	0.6b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))

Compiler

Compiled 3995 to 1682 computations (57.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1/2 (+.f64 b a))
	0.2b	(/.f64 (PI.f64) a)
✓	0.2b	(/.f64 (/.f64 (PI.f64) a) b)
✓	0.2b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (PI.f64) a) b))

series28.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

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

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64`
108×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
87×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

2 → 165

Calls

2 calls:

19.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (PI.f64) a) b))
4.0ms	(/.f64 (/.f64 (PI.f64) a) b)

simplify176.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
631×	`associate-/r/_binary64`
365×	`fma-neg_binary64`
355×	`associate-*r/_binary64`
253×	`associate-*l/_binary64`

Counts

213 → 276

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	4667
1	904	4314
2	2984	4248
3	4586	4248
4	5311	4248

prune330.0ms (6.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	375	1	376
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	377	6	383

Error

Counts

383 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (+.f64 a b))) (/.f64 (PI.f64) (*.f64 a b)))
✓	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (PI.f64) a) b))
▶	0.4b	(.f64 (.f64 (PI.f64) (/.f64 1/2 (+.f64 a b))) (/.f64 (/.f64 1 a) b))
✓	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.8b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	0.6b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))

Compiler

Compiled 7844 to 2762 computations (64.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (+.f64 a b))
✓	0.2b	(.f64 (.f64 (PI.f64) (/.f64 1/2 (+.f64 a b))) (/.f64 (/.f64 1 a) b))
✓	0.2b	(/.f64 (/.f64 1 a) b)
✓	0.4b	(*.f64 (PI.f64) (/.f64 1/2 (+.f64 a b)))

series56.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

18.0ms	(.f64 (.f64 (PI.f64) (/.f64 1/2 (+.f64 a b))) (/.f64 (/.f64 1 a) b))
17.0ms	(*.f64 (PI.f64) (/.f64 1/2 (+.f64 a b)))
12.0ms	(/.f64 1/2 (+.f64 a b))
9.0ms	(/.f64 (/.f64 1 a) b)

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`times-frac_binary64`
113×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
99×	`add-cube-cbrt_binary64`
80×	`add-exp-log_binary64`

Counts

4 → 231

Calls

4 calls:

15.0ms	(.f64 (.f64 (PI.f64) (/.f64 1/2 (+.f64 a b))) (/.f64 (/.f64 1 a) b))
8.0ms	(*.f64 (PI.f64) (/.f64 1/2 (+.f64 a b)))
5.0ms	(/.f64 (/.f64 1 a) b)
4.0ms	(/.f64 1/2 (+.f64 a b))

simplify218.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-def_binary64`
333×	`associate-l_binary64`
319×	`fma-neg_binary64`
317×	`cancel-sign-sub-inv_binary64`
256×	`associate-*r/_binary64`

Counts

327 → 382

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	350	6579
1	934	5876
2	3478	5768
3	4714	5768
4	4994	5768
5	4966	5768

prune360.0ms (7.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	382	0	382
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	382	6	388

Error

Counts

388 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (+.f64 a b))) (/.f64 (PI.f64) (*.f64 a b)))
✓	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (PI.f64) a) b))
✓	0.4b	(.f64 (.f64 (PI.f64) (/.f64 1/2 (+.f64 a b))) (/.f64 (/.f64 1 a) b))
✓	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.8b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	0.6b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))

Compiler

Compiled 8549 to 4655 computations (45.5% saved)

regimes1.1s (21.7%)

Accuracy

Total 0.2b remaining (93.1%)

Threshold costs 0.2b (93.1%)

Counts

325 → 1

Compiler

Compiled 21016 to 13914 computations (33.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	13	17
2	13	17

end82.0ms (1.6%)

Compiler: Compiled 123 to 88 computations (28.5% saved)

Details

analyze316.0ms (6.3%)

sample1.3s (25.2%)

simplify37.0ms (0.7%)

prune7.0ms (0.1%)

localize10.0ms (0.2%)

series49.0ms (1%)

rewrite32.0ms (0.6%)

simplify219.0ms (4.3%)

prune242.0ms (4.8%)

localize7.0ms (0.1%)

series42.0ms (0.8%)

rewrite31.0ms (0.6%)

simplify143.0ms (2.8%)

prune188.0ms (3.7%)

localize7.0ms (0.1%)

series28.0ms (0.5%)

rewrite42.0ms (0.8%)

simplify176.0ms (3.5%)

prune330.0ms (6.5%)

localize8.0ms (0.2%)

series56.0ms (1.1%)

rewrite53.0ms (1.1%)

simplify218.0ms (4.3%)

prune360.0ms (7.1%)

regimes1.1s (21.7%)

simplify2.0ms (0%)

end82.0ms (1.6%)

Profiling