Details

analyze890.0ms (7.4%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
37.4%	62.4%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
65.5%	34.3%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
81.9%	17.9%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample5.1s (42.3%)

Results

2.6s	2033×	body	1024	valid
1.3s	4649×	body	128	valid
770.0ms	1053×	body	512	valid
270.0ms	518×	body	256	valid
7.0ms	3×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify13.0ms (0.1%)

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

prune5.0ms (0%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series48.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

30.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
14.0ms	(*.f64 z (sin.f64 y))
3.0ms	(sin.f64 y)

rewrite123.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`

Counts

3 → 56

Calls

3 calls:

121.0ms	(sin.f64 y)
121.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
121.0ms	(*.f64 z (sin.f64 y))

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

simplify157.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

538×	`fma-neg_binary64`
535×	`sub-neg_binary64`
425×	`distribute-rgt-neg-in_binary64`
364×	`*-commutative_binary64`
358×	`distribute-lft-neg-in_binary64`

Counts

120 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	656
1	140	640
2	398	623
3	1170	621
4	2470	621
5	4497	621
6	5000	621
7	5000	621
8	4908	621

prune128.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Error

0.0b

Counts

82 → 8

Alt Table

Status	Error	Program
	5.8b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	11.0b	(fma.f64 x (cos.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (sin.f64 y))))))
	31.0b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
▶	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	25.7b	(fma.f64 x (cos.f64 y) (*.f64 z (pow.f64 (pow.f64 (sin.f64 y) 3) 1/3)))

Compiler

Compiled 1265 to 559 computations (55.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series355.0ms (3%)

Counts

4 → 84

Calls

4 calls:

305.0ms	(log1p.f64 (sin.f64 y))
30.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
16.0ms	(*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y))))
3.0ms	(expm1.f64 (log1p.f64 (sin.f64 y)))

rewrite93.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

764×	`expm1-log1p-u_binary64`
763×	`log1p-expm1-u_binary64`
236×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`

Counts

4 → 75

Calls

4 calls:

90.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
90.0ms	(*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y))))
90.0ms	(expm1.f64 (log1p.f64 (sin.f64 y)))
90.0ms	(log1p.f64 (sin.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	175	26
2	1994	26
3	5147	26
0	0	0
1	0	0

simplify124.0ms (1%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
509×	`distribute-rgt-neg-in_binary64`
436×	`sub-neg_binary64`
426×	`distribute-lft-neg-in_binary64`
307×	`distribute-lft-out--_binary64`

Counts

159 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	772
1	175	756
2	485	735
3	1451	729
4	3155	729
5	4725	729
6	4993	729

prune208.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Error

0.0b

Counts

116 → 8

Alt Table

Status	Error	Program
	5.8b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	11.0b	(fma.f64 x (cos.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (sin.f64 y))))))
	31.0b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	25.7b	(fma.f64 x (cos.f64 y) (*.f64 z (pow.f64 (pow.f64 (sin.f64 y) 3) 1/3)))

Compiler

Compiled 1672 to 755 computations (54.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.5b	(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)

series3.9s (32.3%)

Counts

2 → 72

Calls

2 calls:

3.5s	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
380.0ms	(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))

rewrite52.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

857×	`log1p-expm1-u_binary64`
857×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`

Counts

2 → 49

Calls

2 calls:

50.0ms	(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))
50.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	204	26
2	2247	26
3	5578	26
0	0	0
1	0	0

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-def_binary64`
376×	`unswap-sqr_binary64`
311×	`associate-r_binary64`
280×	`times-frac_binary64`
221×	`associate-l_binary64`

Counts

121 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	3163
1	822	3059
2	3504	2949
3	5285	2949

prune113.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	190	8	198

Error

0.0b

Counts

198 → 8

Alt Table

Status	Error	Program
▶	5.8b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	11.0b	(fma.f64 x (cos.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (sin.f64 y))))))
	31.0b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	25.7b	(fma.f64 x (cos.f64 y) (*.f64 z (pow.f64 (pow.f64 (sin.f64 y) 3) 1/3)))

Compiler

Compiled 5032 to 2457 computations (51.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	0.1b	(*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))
✓	0.3b	(pow.f64 (sin.f64 y) 3)
✓	20.6b	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

series29.0ms (0.2%)

Counts

4 → 76

Calls

4 calls:

15.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
7.0ms	(*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))
6.0ms	(pow.f64 (sin.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

rewrite54.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

857×	`log1p-expm1-u_binary64`
857×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`

Counts

4 → 82

Calls

4 calls:

52.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
52.0ms	(*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3)))
52.0ms	(pow.f64 (sin.f64 y) 3)
52.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	203	27
2	2247	27
3	5578	27
0	0	0
1	0	0

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-neg_binary64`
539×	`sub-neg_binary64`
494×	`distribute-rgt-neg-in_binary64`
413×	`distribute-lft-neg-in_binary64`
304×	`neg-mul-1_binary64`

Counts

158 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	748
1	176	728
2	511	707
3	1461	705
4	2985	705
5	4548	705
6	4972	705
7	4997	705
8	4912	705

prune68.0ms (0.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	114	8	122

Error

0.0b

Counts

122 → 8

Alt Table

Status	Error	Program
✓	5.8b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	11.0b	(fma.f64 x (cos.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (sin.f64 y))))))
	31.0b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	31.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	25.7b	(fma.f64 x (cos.f64 y) (*.f64 z (pow.f64 (pow.f64 (sin.f64 y) 3) 1/3)))

Compiler

Compiled 1687 to 759 computations (55% saved)

regimes207.0ms (1.7%)

Accuracy

Total 0.1b remaining (42.8%)

Threshold costs 0.1b (42.8%)

Counts

57 → 1

Compiler

Compiled 2944 to 1994 computations (32.3% 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

end115.0ms (1%)

Compiler: Compiled 135 to 93 computations (31.1% saved)

Details

analyze890.0ms (7.4%)

sample5.1s (42.3%)

simplify13.0ms (0.1%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series48.0ms (0.4%)

rewrite123.0ms (1%)

simplify157.0ms (1.3%)

prune128.0ms (1.1%)

localize20.0ms (0.2%)

series355.0ms (3%)

rewrite93.0ms (0.8%)

simplify124.0ms (1%)

prune208.0ms (1.7%)

localize20.0ms (0.2%)

series3.9s (32.3%)

rewrite52.0ms (0.4%)

simplify87.0ms (0.7%)

prune113.0ms (0.9%)

localize10.0ms (0.1%)

series29.0ms (0.2%)

rewrite54.0ms (0.4%)

simplify117.0ms (1%)

prune68.0ms (0.6%)

regimes207.0ms (1.7%)

simplify2.0ms (0%)

end115.0ms (1%)

Profiling