Details

analyze323.0ms (6.8%)

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
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)

sample1.2s (25.7%)

Results

1.1s	8256×	body	128	valid
51.0ms	372×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify38.0ms (0.8%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
▶	0.3b	(*.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

16.6b

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

▶

0.3b

(*.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)))
✓	0.2b	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))

series80.0ms (1.7%)

Counts

4 → 72

Calls

4 calls:

49.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
20.0ms	(/.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 (0.7%)

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:

15.0ms	(*.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))

simplify212.0ms (4.4%)

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

prune234.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	232	7	239

Error

Counts

239 → 7

Alt Table

Status	Error	Program
	0.3b	(/.f64 (*.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (/.f64 1/2 (+.f64 a b))) (-.f64 b a))
	16.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.4b	(.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))))
	30.9b	(.f64 (/.f64 (PI.f64) (.f64 a a)) (-.f64 (/.f64 1/2 b) (/.f64 1/2 a)))
▶	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (.f64 (PI.f64) (/.f64 1 a))) (-.f64 b a)))
✓	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

Compiler

Compiled 6896 to 2615 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))

series39.0ms (0.8%)

Counts

3 → 48

Calls

3 calls:

17.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
11.0ms	(/.f64 1/2 (+.f64 b a))
11.0ms	(/.f64 (PI.f64) (*.f64 a b))

rewrite25.0ms (0.5%)

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:

11.0ms	(.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))

simplify104.0ms (2.2%)

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

prune166.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	194	7	201

Error

Counts

201 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 b a)) (/.f64 (PI.f64) (*.f64 a b))))
✓	0.3b	(*.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 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
	16.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2))) (/.f64 (PI.f64) (.f64 a b)))
✓	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.8b	(.f64 1/2 (/.f64 (PI.f64) (.f64 (*.f64 a b) (+.f64 a b))))

Compiler

Compiled 3967 to 1673 computations (57.8% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1/2 (+.f64 b a))
✓	0.2b	(/.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
✓	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64))

series34.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(/.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
16.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`
18×	`associate-l_binary64`
17×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

2 → 67

Calls

2 calls:

8.0ms	(/.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
7.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64))

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
436×	`fma-def_binary64`
365×	`associate-/r/_binary64`
319×	`times-frac_binary64`
227×	`cancel-sign-sub-inv_binary64`

Counts

115 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2922
1	591	2531
2	2344	2399
3	4501	2399
4	5117	2399

prune173.0ms (3.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	205	7	212

Error

Counts

212 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 b a)) (/.f64 (PI.f64) (*.f64 a b))))
✓	0.3b	(*.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 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
	16.6b	(.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
▶	0.4b	(.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2))) (/.f64 (PI.f64) (.f64 a b)))
✓	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.8b	(.f64 1/2 (/.f64 (PI.f64) (.f64 (*.f64 a b) (+.f64 a b))))

Compiler

Compiled 4280 to 2054 computations (52% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2))) (/.f64 (PI.f64) (.f64 a b)))
	0.4b	(/.f64 (PI.f64) (*.f64 a b))
✓	0.4b	(/.f64 (+.f64 b a) (sqrt.f64 1/2))
✓	0.5b	(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2)))

series65.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2))) (/.f64 (PI.f64) (.f64 a b)))
22.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2)))
12.0ms	(/.f64 (+.f64 b a) (sqrt.f64 1/2))

rewrite128.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

685×	`times-frac_binary64`
502×	`*-un-lft-identity_binary64`
356×	`add-sqr-sqrt_binary64`
347×	`sqrt-prod_binary64`
332×	`add-cube-cbrt_binary64`

Counts

3 → 488

Calls

3 calls:

35.0ms	(.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2))) (/.f64 (PI.f64) (.f64 a b)))
10.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2)))
6.0ms	(/.f64 (+.f64 b a) (sqrt.f64 1/2))

simplify368.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

489×	`associate-*l/_binary64`
410×	`associate-*r/_binary64`
365×	`associate-/l*_binary64`
320×	`associate-/r/_binary64`
313×	`times-frac_binary64`

Counts

560 → 579

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	15867
1	1190	13881
2	4577	13441
3	4926	13441
4	5001	13441

prune638.0ms (13.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	603	2	605
Fresh	2	1	3
Picked	1	0	1
Done	0	3	3
Total	606	6	612

Error

Counts

612 → 6

Alt Table

Status	Error	Program
	0.4b	(*.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 b a) (sqrt.f64 1/2))) (/.f64 (/.f64 (PI.f64) a) b))
	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (/.f64 (sqrt.f64 1/2) (+.f64 a b)) (/.f64 (PI.f64) (*.f64 a b))))
✓	0.2b	(/.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))
✓	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.8b	(.f64 1/2 (/.f64 (PI.f64) (.f64 (*.f64 a b) (+.f64 a b))))
✓	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

Compiler

Compiled 16678 to 9438 computations (43.4% saved)

regimes639.0ms (13.4%)

Accuracy

Total 0.2b remaining (91.3%)

Threshold costs 0.2b (91.3%)

Counts

197 → 1

Compiler

Compiled 11617 to 8100 computations (30.3% 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

end85.0ms (1.8%)

Compiler: Compiled 119 to 84 computations (29.4% saved)

Details

analyze323.0ms (6.8%)

sample1.2s (25.7%)

simplify38.0ms (0.8%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series80.0ms (1.7%)

rewrite34.0ms (0.7%)

simplify212.0ms (4.4%)

prune234.0ms (4.9%)

localize7.0ms (0.1%)

series39.0ms (0.8%)

rewrite25.0ms (0.5%)

simplify104.0ms (2.2%)

prune166.0ms (3.5%)

localize12.0ms (0.3%)

series34.0ms (0.7%)

rewrite20.0ms (0.4%)

simplify92.0ms (1.9%)

prune173.0ms (3.6%)

localize9.0ms (0.2%)

series65.0ms (1.4%)

rewrite128.0ms (2.7%)

simplify368.0ms (7.7%)

prune638.0ms (13.4%)

regimes639.0ms (13.4%)

simplify2.0ms (0%)

end85.0ms (1.8%)

Profiling