Details

analyze1.2s (10.7%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample120.0ms (1.1%)

Algorithm

1×

intervals

Results

34.0ms	75×	body	1024	valid
21.0ms	43×	body	1024	invalid
14.0ms	140×	body	128	valid
8.0ms	29×	body	512	valid
6.0ms	21×	body	512	invalid
2.0ms	12×	body	256	valid
2.0ms	21×	body	128	invalid
2.0ms	11×	body	256	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune4.0ms (0%)

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
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 th)
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

3 → 94

Calls

3 calls:

8.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
3.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	(cos.f64 th)

series152.0ms (1.4%)

Counts

3 → 64

Calls

3 calls:

105.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
46.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	(cos.f64 th)

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-l_binary64`
420×	`associate-r_binary64`
337×	`unswap-sqr_binary64`
336×	`associate-/l*_binary64`
276×	`associate-*r/_binary64`

Counts

158 → 301

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	3431
1	398	3117
2	1373	3069
3	4414	3069
4	5205	3069

prune169.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	294	7	301
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	295	8	303

Error

Counts

303 → 8

Alt Table

Status	Error	Program
	1.1b	(.f64 (cos.f64 th) (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))) (cbrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))
	0.5b	(.f64 (expm1.f64 (log1p.f64 (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 4101 to 1935 computations (52.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
44×	`associate-l_binary64`
44×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`

Counts

3 → 135

Calls

3 calls:

12.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
7.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

series140.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

62.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
61.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
16.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify158.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-*l/_binary64`
511×	`associate-/l*_binary64`
431×	`fma-def_binary64`
425×	`associate-*r/_binary64`
240×	`fma-neg_binary64`

Counts

187 → 340

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3496
1	559	3164
2	1620	3148
3	4427	3146
4	4999	3146
5	4986	3146

prune276.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	402	1	403
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	403	8	411

Error

Counts

411 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (expm1.f64 (log1p.f64 (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
✓	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 7649 to 4221 computations (44.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))
✓	0.6b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
✓	0.6b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite134.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

1137×	`sqrt-prod_binary64`
1119×	`times-frac_binary64`
610×	`add-sqr-sqrt_binary64`
576×	`*-un-lft-identity_binary64`
576×	`add-cube-cbrt_binary64`

Counts

3 → 711

Calls

3 calls:

40.0ms

(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 a2 a2))

12.0ms

(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

4.0ms

(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

series95.0ms (0.9%)

Counts

3 → 48

Calls

3 calls:

60.0ms

(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 a2 a2))

20.0ms

(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

14.0ms

(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify729.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
456×	`associate-*l/_binary64`
399×	`associate-/r/_binary64`
390×	`*-commutative_binary64`
387×	`associate-/l/_binary64`

Counts

759 → 1456

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	471	21838
1	1311	20764
2	2730	19880
3	3982	19680
4	4986	19680
5	4977	19680

prune1.0s (9.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1582	0	1582
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1582	8	1590

Error

Counts

1590 → 8

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (expm1.f64 (log1p.f64 (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
✓	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
✓	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 32336 to 21130 computations (34.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (expm1.f64 (log1p.f64 (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 th)))
✓	0.3b	(log1p.f64 (cos.f64 th))
	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
20×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 66

Calls

3 calls:

7.0ms	(.f64 (expm1.f64 (log1p.f64 (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
0.0ms	(log1p.f64 (cos.f64 th))
0.0ms	(expm1.f64 (log1p.f64 (cos.f64 th)))

series1.1s (10%)

Counts

3 → 60

Calls

3 calls:

593.0ms	(.f64 (expm1.f64 (log1p.f64 (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
261.0ms	(log1p.f64 (cos.f64 th))
250.0ms	(expm1.f64 (log1p.f64 (cos.f64 th)))

simplify122.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

523×	`distribute-rgt-in_binary64`
454×	`distribute-lft-in_binary64`
396×	`fma-def_binary64`
260×	`times-frac_binary64`
145×	`associate-r_binary64`

Counts

126 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	3095
1	521	2880
2	1897	2799
3	4821	2799
4	5027	2799

prune178.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	366	7	373

Error

Counts

373 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
✓	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
	0.5b	(.f64 (expm1.f64 (log1p.f64 (cos.f64 th))) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
✓	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 4991 to 2301 computations (53.9% saved)

regimes1.8s (16.7%)

Accuracy

Total 0.4b remaining (90.7%)

Threshold costs 0.4b (90.7%)

Compiler

Compiled 36300 to 24758 computations (31.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
1	18	48
2	18	48

end7.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 99 to 63 computations (36.4% saved)

sample3.3s (30.3%)

Algorithm

1×

intervals

Results

849.0ms	1830×	body	1024	valid
710.0ms	1550×	body	1024	invalid
467.0ms	4831×	body	128	valid
287.0ms	901×	body	512	valid
222.0ms	762×	body	512	invalid
85.0ms	436×	body	256	valid
81.0ms	406×	body	256	invalid
68.0ms	681×	body	128	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 213 to 146 computations (31.5% saved)

Details

analyze1.2s (10.7%)

sample120.0ms (1.1%)

simplify17.0ms (0.2%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite19.0ms (0.2%)

series152.0ms (1.4%)

simplify128.0ms (1.2%)

prune169.0ms (1.5%)

localize11.0ms (0.1%)

rewrite30.0ms (0.3%)

series140.0ms (1.3%)

simplify158.0ms (1.4%)

prune276.0ms (2.5%)

localize15.0ms (0.1%)

rewrite134.0ms (1.2%)

series95.0ms (0.9%)

simplify729.0ms (6.6%)

prune1.0s (9.2%)

localize13.0ms (0.1%)

rewrite11.0ms (0.1%)

series1.1s (10%)

simplify122.0ms (1.1%)

prune178.0ms (1.6%)

regimes1.8s (16.7%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample3.3s (30.3%)

Profiling