Details

analyze503.0ms (9.3%)

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
0%	99.9%	0.1%	6
37.4%	62.4%	0.1%	7
43.7%	56.2%	0.1%	8
43.7%	56.2%	0.1%	9
65.5%	34.3%	0.1%	10
70.2%	29.6%	0.1%	11
70.2%	29.6%	0.1%	12
81.9%	17.9%	0.1%	13
84.6%	15.2%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.2s (58.9%)

Results

1.6s	2117×	body	1024	valid
901.0ms	4606×	body	128	valid
481.0ms	1046×	body	512	valid
140.0ms	483×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12
3	16	12

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 y)
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.2b	(*.f64 z (cos.f64 y))

series25.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

15.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
8.0ms	(*.f64 z (cos.f64 y))
2.0ms	(cos.f64 y)

rewrite49.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

56× egg-rr

Counts

3 → 56

Calls

2 calls:

47.0ms	((.f64 z (cos.f64 y)) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (cos.f64 y))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	156	21
2	1801	21
3	5105	21
0	0	0
1	0	0

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

689×	`distribute-rgt-neg-in_binary64`
583×	`distribute-lft-neg-in_binary64`
474×	`fma-neg_binary64`
354×	`sub-neg_binary64`
305×	`*-commutative_binary64`

Counts

120 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	644
1	132	637
2	372	620
3	1182	619
4	2838	619
5	4978	619
6	4984	619
7	4942	619

prune60.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	8	81

Error

0.1b

Counts

81 → 8

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.4b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	33.8b	(fma.f64 y x (fma.f64 (fma.f64 (.f64 y y) -1/2 1) z (.f64 x (*.f64 (pow.f64 y 3) -1/6))))

Compiler

Compiled 1283 to 562 computations (56.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 y)
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
✓	0.1b	(*.f64 (sin.f64 y) x)

series22.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
7.0ms	(*.f64 (sin.f64 y) x)

rewrite44.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

38× egg-rr

Counts

2 → 38

Calls

2 calls:

43.0ms	((.f64 (sin.f64 y) x) (fma.f64 (cos.f64 y) z (.f64 (sin.f64 y) x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1801	18
3	5105	18
0	0	0
1	0	0

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
602×	`distribute-rgt-neg-in_binary64`
555×	`distribute-lft-neg-in_binary64`
523×	`associate-l_binary64`
430×	`associate-r_binary64`

Counts

78 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	480
1	117	472
2	328	460
3	963	451
4	3204	451
5	4809	451
6	5026	451

prune111.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Error

0.1b

Counts

90 → 8

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))))
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	0.6b	(fma.f64 (cos.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (sin.f64 y) x)) 3))
	1.4b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))

Compiler

Compiled 1281 to 541 computations (57.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	0.1b	(*.f64 (sin.f64 y) x)
✓	0.1b	(expm1.f64 (log1p.f64 (cos.f64 y)))
✓	0.4b	(log1p.f64 (cos.f64 y))

series234.0ms (4.3%)

Counts

3 → 60

Calls

3 calls:

215.0ms	(log1p.f64 (cos.f64 y))
15.0ms	(fma.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
4.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

rewrite46.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

60× egg-rr

Counts

3 → 60

Calls

2 calls:

45.0ms	((log1p.f64 (cos.f64 y)) (expm1.f64 (log1p.f64 (cos.f64 y))) (fma.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	175	20
2	1994	20
3	5150	20
0	0	0
1	0	0

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

690×	`distribute-rgt-neg-in_binary64`
573×	`distribute-lft-neg-in_binary64`
393×	`fma-neg_binary64`
386×	`sub-neg_binary64`
313×	`distribute-lft-out--_binary64`

Counts

120 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	578
1	143	574
2	385	565
3	1209	564
4	2770	564
5	4948	564

prune119.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	108	9	117

Error

0.1b

Counts

117 → 9

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))))
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	0.6b	(fma.f64 (cos.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (sin.f64 y) x)) 3))
	1.4b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	1.2b	(fma.f64 (expm1.f64 (.f64 (cbrt.f64 (log1p.f64 (cos.f64 y))) (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 y))) 2))) z (.f64 (sin.f64 y) x))
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))

Compiler

Compiled 1790 to 753 computations (57.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
✓	0.2b	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series32.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

14.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
13.0ms	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
3.0ms	(expm1.f64 (cos.f64 y))
2.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

rewrite51.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

75× egg-rr

Counts

4 → 75

Calls

2 calls:

49.0ms	((expm1.f64 (cos.f64 y)) (log1p.f64 (expm1.f64 (cos.f64 y))) (.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))) (fma.f64 x (sin.f64 y) (.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	175	26
2	1994	26
3	5150	26
0	0	0
1	0	0

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
340×	`distribute-rgt-neg-in_binary64`
332×	`distribute-lft-neg-in_binary64`
248×	`neg-mul-1_binary64`
226×	`cancel-sign-sub-inv_binary64`

Counts

159 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	796
1	188	785
2	540	761
3	1787	754
4	4877	754
5	5039	754

prune87.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	108	9	117

Error

0.1b

Counts

117 → 9

Alt Table

Status	Error	Program
	0.9b	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) z)) 3))
✓	0.2b	(fma.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))))
	33.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	0.6b	(fma.f64 (cos.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (sin.f64 y) x)) 3))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	1.2b	(fma.f64 (expm1.f64 (.f64 (cbrt.f64 (log1p.f64 (cos.f64 y))) (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 y))) 2))) z (.f64 (sin.f64 y) x))
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))

Compiler

Compiled 1620 to 713 computations (56% saved)

regimes352.0ms (6.5%)

Accuracy

Total 0.1b remaining (47.1%)

Threshold costs 0.1b (47.1%)

Counts

83 → 1

Compiler

Compiled 4456 to 3058 computations (31.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end147.0ms (2.7%)

Compiler: Compiled 157 to 109 computations (30.6% saved)

Details

analyze503.0ms (9.3%)

sample3.2s (58.9%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series25.0ms (0.5%)

rewrite49.0ms (0.9%)

simplify96.0ms (1.8%)

prune60.0ms (1.1%)

localize11.0ms (0.2%)

series22.0ms (0.4%)

rewrite44.0ms (0.8%)

simplify77.0ms (1.4%)

prune111.0ms (2.1%)

localize11.0ms (0.2%)

series234.0ms (4.3%)

rewrite46.0ms (0.9%)

simplify52.0ms (1%)

prune119.0ms (2.2%)

localize10.0ms (0.2%)

series32.0ms (0.6%)

rewrite51.0ms (0.9%)

simplify64.0ms (1.2%)

prune87.0ms (1.6%)

regimes352.0ms (6.5%)

simplify2.0ms (0%)

end147.0ms (2.7%)

Profiling