Details

analyze378.0ms (6.4%)

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
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)

sample1.4s (23.9%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify40.0ms (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

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)))
	13.1b	(.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)))

13.1b

(*.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)

localize16.0ms (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)

series104.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

42.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
37.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
20.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
5.0ms	(/.f64 (PI.f64) a)

rewrite75.0ms (1.3%)

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:

31.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
8.0ms	(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
4.0ms	(/.f64 (PI.f64) a)
1.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))

simplify421.0ms (7.2%)

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	5398
1	676	4819
2	2133	4749
3	4629	4748
4	4989	4748
5	4998	4748
6	4972	4748

prune455.0ms (7.7%)

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

0.0b

Counts

239 → 8

Alt Table

Status	Error	Program
	22.7b	(.f64 (sqrt.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))) (sqrt.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))))
	25.7b	(.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 a 2) b)))
	0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a 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)))
	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	0.6b	(.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)))))
	26.5b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a (pow.f64 b 2))))
	0.3b	(.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 6986 to 2663 computations (61.9% saved)

localize23.0ms (0.4%)

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 a b)) (/.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)

series35.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

35.0ms

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

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
21×	`associate-r_binary64`
18×	`associate-l_binary64`

Counts

1 → 65

Calls

1 calls:

27.0ms

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

simplify166.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-/l*_binary64`
373×	`times-frac_binary64`
307×	`fma-neg_binary64`
285×	`fma-def_binary64`
257×	`associate-/l/_binary64`

Counts

89 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3185
1	550	2861
2	1817	2795
3	4773	2795
4	4963	2795

prune479.0ms (8.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	213	8	221

Error

0.0b

Counts

221 → 8

Alt Table

Status	Error	Program
	22.7b	(.f64 (sqrt.f64 (.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))) (sqrt.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))))
	25.7b	(.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 a 2) b)))
	0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a 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)))
▶	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	0.6b	(.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)))))
	26.5b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a (pow.f64 b 2))))
	0.3b	(.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 6248 to 2579 computations (58.7% saved)

localize23.0ms (0.4%)

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))
✓	0.3b	(/.f64 (PI.f64) b)
	0.3b	(/.f64 (PI.f64) a)

series74.0ms (1.3%)

Counts

3 → 48

Calls

3 calls:

38.0ms	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
32.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
4.0ms	(/.f64 (PI.f64) b)

rewrite84.0ms (1.4%)

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:

35.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
24.0ms	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
4.0ms	(/.f64 (PI.f64) b)

simplify198.0ms (3.4%)

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

prune388.0ms (6.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	238	7	245

Error

Counts

245 → 7

Alt Table

Status	Error	Program
	0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.3b	(/.f64 (.f64 1/2 (.f64 (PI.f64) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
	0.5b	(/.f64 1/2 (/.f64 (+.f64 b a) (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) 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)))
	30.4b	(/.f64 (.f64 1/2 (.f64 (sqrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (/.f64 (sqrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))) (-.f64 b a)))) (+.f64 b a))
▶	0.2b	(/.f64 (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) -1/2) (-.f64 (neg.f64 b) a))
	0.3b	(.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 6680 to 1867 computations (72.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series21.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

20.0ms

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

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-/r*_binary64`

Counts

1 → 34

Calls

1 calls:

23.0ms

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

simplify96.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

718×	`times-frac_binary64`
496×	`associate-/l/_binary64`
384×	`fma-neg_binary64`
226×	`fma-def_binary64`
180×	`distribute-rgt-in_binary64`

Counts

58 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2078
1	388	1806
2	1484	1736
3	4931	1736
4	5165	1736

prune335.0ms (5.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	231	6	237

Error

Counts

237 → 6

Alt Table

Status	Error	Program
	0.2b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (PI.f64) (.f64 a b)))
	0.3b	(/.f64 (.f64 1/2 (.f64 (PI.f64) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
	0.5b	(/.f64 1/2 (/.f64 (+.f64 b a) (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) 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)))
	0.3b	(/.f64 (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 1 (/.f64 b (PI.f64)))) (-.f64 b a)) -1/2) (-.f64 (neg.f64 b) a))
	0.3b	(.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 6590 to 1739 computations (73.6% saved)

regimes771.0ms (13.1%)

Accuracy

Total 0.2b remaining (90%)

Threshold costs 0.2b (90%)

Counts

154 → 1

Compiler

Compiled 11395 to 7092 computations (37.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	19	19
2	26	19
3	33	19
4	36	19
5	37	19
6	37	19

end200.0ms (3.4%)

Compiler: Compiled 149 to 103 computations (30.9% saved)

Details

analyze378.0ms (6.4%)

sample1.4s (23.9%)

simplify40.0ms (0.7%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

series104.0ms (1.8%)

rewrite75.0ms (1.3%)

simplify421.0ms (7.2%)

prune455.0ms (7.7%)

localize23.0ms (0.4%)

series35.0ms (0.6%)

rewrite38.0ms (0.7%)

simplify166.0ms (2.8%)

prune479.0ms (8.2%)

localize23.0ms (0.4%)

series74.0ms (1.3%)

rewrite84.0ms (1.4%)

simplify198.0ms (3.4%)

prune388.0ms (6.6%)

localize11.0ms (0.2%)

series21.0ms (0.3%)

rewrite27.0ms (0.5%)

simplify96.0ms (1.6%)

prune335.0ms (5.7%)

regimes771.0ms (13.1%)

simplify6.0ms (0.1%)

end200.0ms (3.4%)

Profiling