Details

analyze321.0ms (8.8%)

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 (34%)

Results

1.1s	8256×	body	128	valid
45.0ms	353×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify36.0ms (1%)

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
	14.6b	(.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

14.6b

(*.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)

localize11.0ms (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))
✓	0.3b	(/.f64 (PI.f64) a)

series47.0ms (1.3%)

Counts

4 → 72

Calls

4 calls:

18.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
18.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.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))
3.0ms	(/.f64 (PI.f64) a)

rewrite33.0ms (0.9%)

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))

simplify202.0ms (5.6%)

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

prune258.0ms (7.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	227	10	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	10	239

Error

Counts

239 → 10

Alt Table

Status	Error	Program
	22.4b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a (*.f64 a b))))
	0.3b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.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))))
	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 1 (/.f64 a (PI.f64)))) (-.f64 b a)))
	31.6b	(.f64 (/.f64 (PI.f64) (.f64 b b)) (-.f64 (/.f64 1/2 a) (/.f64 1/2 b)))
	0.3b	(/.f64 (*.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (/.f64 1/2 (+.f64 a b))) (-.f64 b a))
	0.7b	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (cbrt.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)))) (/.f64 1/2 (+.f64 a b))) (cbrt.f64 (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
▶	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 b a)) (cbrt.f64 (+.f64 b a)))) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 1/2 (cbrt.f64 (+.f64 a b)))))
	0.5b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) a)) (cbrt.f64 (/.f64 (PI.f64) a))) (cbrt.f64 (/.f64 (PI.f64) a)))) (-.f64 b a)))

Compiler

Compiled 7108 to 2717 computations (61.8% saved)

localize6.0ms (0.2%)

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)))
✓	0.7b	(/.f64 (PI.f64) (*.f64 a b))

series38.0ms (1.1%)

Counts

3 → 48

Calls

3 calls:

17.0ms	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
11.0ms	(/.f64 (PI.f64) (*.f64 a b))
10.0ms	(/.f64 1/2 (+.f64 b a))

rewrite24.0ms (0.7%)

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))

simplify105.0ms (2.9%)

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

prune193.0ms (5.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	197	7	204

Error

Counts

204 → 7

Alt Table

Status	Error	Program
	31.6b	(.f64 (/.f64 (PI.f64) (.f64 b b)) (-.f64 (/.f64 1/2 a) (/.f64 1/2 b)))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (/.f64 (.f64 a b) (PI.f64))))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (/.f64 1 a) (/.f64 (PI.f64) b)))
	0.6b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	0.3b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.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))))
▶	0.2b	(/.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64)) (.f64 a b))

Compiler

Compiled 3994 to 1687 computations (57.8% saved)

localize7.0ms (0.2%)

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))

series32.0ms (0.9%)

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 (0.5%)

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:

7.0ms	(/.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 (2.5%)

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

prune172.0ms (4.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	206	6	212

Error

Counts

212 → 6

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (.f64 a b) (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64))))
▶	0.2b	(/.f64 (/.f64 (.f64 1/2 (PI.f64)) (+.f64 b a)) (.f64 a b))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (/.f64 1 a) (/.f64 (PI.f64) b)))
	0.6b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	0.3b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	0.2b	(/.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (*.f64 a b) (PI.f64)))

Compiler

Compiled 4266 to 2037 computations (52.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series32.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(/.f64 (/.f64 (.f64 1/2 (PI.f64)) (+.f64 b a)) (.f64 a b))
15.0ms	(/.f64 (*.f64 1/2 (PI.f64)) (+.f64 b a))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`
22×	`times-frac_binary64`
16×	`*-un-lft-identity_binary64`
12×	`cbrt-undiv_binary64`

Counts

2 → 73

Calls

2 calls:

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

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-*l/_binary64`
482×	`associate-/r/_binary64`
473×	`fma-def_binary64`
229×	`cancel-sign-sub-inv_binary64`
201×	`times-frac_binary64`

Counts

121 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	3142
1	606	2756
2	2234	2616
3	5309	2616

prune114.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Error

Counts

152 → 5

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (.f64 a b) (.f64 (/.f64 1/2 (+.f64 b a)) (PI.f64))))
✓	0.2b	(/.f64 (/.f64 (.f64 1/2 (PI.f64)) (+.f64 b a)) (.f64 a b))
	0.3b	(.f64 (/.f64 1/2 (+.f64 b a)) (.f64 (/.f64 1 a) (/.f64 (PI.f64) b)))
	0.2b	(/.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (*.f64 a b) (PI.f64)))
	3.5b	(/.f64 (/.f64 (/.f64 (*.f64 1/2 (PI.f64)) (+.f64 b a)) a) b)

Compiler

Compiled 2981 to 1359 computations (54.4% saved)

regimes485.0ms (13.3%)

Accuracy

Total 0.2b remaining (80%)

Threshold costs 0.2b (80%)

Counts

170 → 1

Compiler

Compiled 9511 to 6375 computations (33% saved)

simplify2.0ms (0.1%)

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

end65.0ms (1.8%)

Compiler: Compiled 95 to 67 computations (29.5% saved)

Details

analyze321.0ms (8.8%)

sample1.2s (34%)

simplify36.0ms (1%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

series47.0ms (1.3%)

rewrite33.0ms (0.9%)

simplify202.0ms (5.6%)

prune258.0ms (7.1%)

localize6.0ms (0.2%)

series38.0ms (1.1%)

rewrite24.0ms (0.7%)

simplify105.0ms (2.9%)

prune193.0ms (5.3%)

localize7.0ms (0.2%)

series32.0ms (0.9%)

rewrite20.0ms (0.5%)

simplify92.0ms (2.5%)

prune172.0ms (4.7%)

localize6.0ms (0.2%)

series32.0ms (0.9%)

rewrite19.0ms (0.5%)

simplify75.0ms (2.1%)

prune114.0ms (3.1%)

regimes485.0ms (13.3%)

simplify2.0ms (0.1%)

end65.0ms (1.8%)

Profiling