Details

analyze688.0ms (9.2%)

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)

sample56.0ms (0.8%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 49 to 37 computations (24.5% saved)

simplify57.0ms (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

prune8.0ms (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
▶	0.3b	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	11.2b	(.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

▶

0.3b

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

11.2b

(*.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)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	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)))
✓	0.2b	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) 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 (1.4%)

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)))
19.0ms	(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
5.0ms	(/.f64 (PI.f64) a)

rewrite73.0ms (1%)

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:

32.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
11.0ms	(/.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))

simplify379.0ms (5.1%)

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

prune517.0ms (7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	230	7	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

Counts

239 → 7

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	0.7b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))) (/.f64 (-.f64 b a) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) 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 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (*.f64 (/.f64 (cbrt.f64 1/2) (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	39.0b	(.f64 (/.f64 1/2 (+.f64 (pow.f64 b 3) (pow.f64 a 3))) (.f64 (+.f64 (.f64 b b) (-.f64 (.f64 a a) (*.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.3b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
	6.1b	(/.f64 (.f64 1/2 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (.f64 (+.f64 b a) (-.f64 b a)))

Compiler

Compiled 7018 to 2685 computations (61.7% saved)

localize20.0ms (0.3%)

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) a)
✓	0.3b	(/.f64 (PI.f64) b)

series76.0ms (1%)

Counts

3 → 48

Calls

3 calls:

37.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
35.0ms	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
5.0ms	(/.f64 (PI.f64) b)

rewrite124.0ms (1.7%)

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:

40.0ms	(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
40.0ms	(/.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)

simplify321.0ms (4.3%)

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

prune468.0ms (6.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	237	7	244

Error

Counts

244 → 7

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
	0.7b	(.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (.f64 (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (cbrt.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)))) (/.f64 (-.f64 b a) (cbrt.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))))
	6.1b	(/.f64 (.f64 1/2 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (.f64 (+.f64 b a) (-.f64 b a)))
▶	0.2b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.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))))
	39.0b	(.f64 (/.f64 1/2 (+.f64 (pow.f64 b 3) (pow.f64 a 3))) (.f64 (+.f64 (.f64 b b) (-.f64 (.f64 a a) (*.f64 b a))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))))
	0.3b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

Compiler

Compiled 6731 to 1900 computations (71.8% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
✓	0.1b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
✓	0.9b	(/.f64 (PI.f64) (*.f64 a b))

series86.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

34.0ms	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
28.0ms	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
24.0ms	(/.f64 (PI.f64) (*.f64 a b))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 84

Calls

3 calls:

14.0ms	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.f64 b a))
12.0ms	(.f64 1/2 (/.f64 (PI.f64) (.f64 a b)))
6.0ms	(/.f64 (PI.f64) (*.f64 a b))

simplify154.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

860×	`associate-/r*_binary64`
606×	`associate-/l/_binary64`
435×	`associate-/r/_binary64`
248×	`fma-def_binary64`
140×	`cancel-sign-sub-inv_binary64`

Counts

108 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2343
1	474	2001
2	1614	1934
3	4969	1934

prune250.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	126	6	132

Error

Counts

132 → 6

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (*.f64 a b)))) (+.f64 b a))
	0.5b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	6.1b	(/.f64 (.f64 1/2 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (.f64 (+.f64 b a) (-.f64 b a)))
✓	0.2b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.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))
▶	0.3b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

Compiler

Compiled 2428 to 1001 computations (58.8% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

36.0ms

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

rewrite47.0ms (0.6%)

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:

30.0ms

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

simplify186.0ms (2.5%)

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

prune386.0ms (5.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	213	6	219

Error

Counts

219 → 6

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (*.f64 a b)))) (+.f64 b a))
	0.5b	(/.f64 (.f64 1/2 (PI.f64)) (.f64 (+.f64 b a) (*.f64 a b)))
	6.1b	(/.f64 (.f64 1/2 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))) (.f64 (+.f64 b a) (-.f64 b a)))
✓	0.2b	(/.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 a b))) (+.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))
✓	0.3b	(*.f64 (/.f64 1/2 (+.f64 a b)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))

Compiler

Compiled 6024 to 2435 computations (59.6% saved)

regimes1.5s (19.6%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Counts

230 → 1

Compiler

Compiled 17431 to 10620 computations (39.1% saved)

simplify4.0ms (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

end1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample1.8s (24.7%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
50.0ms	326×	body	128	invalid

Compiler

Compiled 141 to 98 computations (30.5% saved)

Details

analyze688.0ms (9.2%)

sample56.0ms (0.8%)

simplify57.0ms (0.8%)

prune8.0ms (0.1%)

localize27.0ms (0.4%)

series104.0ms (1.4%)

rewrite73.0ms (1%)

simplify379.0ms (5.1%)

prune517.0ms (7%)

localize20.0ms (0.3%)

series76.0ms (1%)

rewrite124.0ms (1.7%)

simplify321.0ms (4.3%)

prune468.0ms (6.3%)

localize13.0ms (0.2%)

series86.0ms (1.2%)

rewrite43.0ms (0.6%)

simplify154.0ms (2.1%)

prune250.0ms (3.4%)

localize22.0ms (0.3%)

series36.0ms (0.5%)

rewrite47.0ms (0.6%)

simplify186.0ms (2.5%)

prune386.0ms (5.2%)

regimes1.5s (19.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.8s (24.7%)

Profiling