Details

analyze634.0ms (13.3%)

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
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.2s (46.6%)

Results

963.0ms	1334×	body	1024	valid
897.0ms	5970×	body	128	valid
247.0ms	599×	body	512	valid
101.0ms	349×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess20.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

24×	`fma-def_binary64`
18×	`+-commutative_binary64`
12×	`associate-+r+_binary64`
12×	`associate-+l+_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
1	42	48
2	78	48
3	102	48
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	23	12
3	29	12

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

Compiler

Compiled 44 to 26 computations (40.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.4%)

Counts

2 → 60

Calls

15 calls:

3.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))	z	-inf
1.0ms	(*.f64 z (cos.f64 y))	z	-inf
1.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))	x	-inf
1.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))	x	inf
1.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))	x	0

rewrite52.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

497×	`log-prod_binary64`
490×	`fma-def_binary64`
236×	`fma-neg_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	198	18
2	2851	18

Stop Event

1×	node limit

Counts

2 → 100

simplify40.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
464×	`distribute-rgt-neg-in_binary64`
324×	`fma-neg_binary64`
305×	`sub-neg_binary64`
228×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	589
1	110	586
2	338	575
3	1307	564
4	3991	564

Stop Event

1×	node limit

Counts

160 → 121

prune74.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	7	122

Error

0.0b

Counts

122 → 7

Alt Table

Status	Error	Program
	0.6b	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) (+.f64 x (sin.f64 y)))
	42.3b	(/.f64 (+.f64 (pow.f64 (+.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (fma.f64 (.f64 z (cos.f64 y)) (-.f64 (*.f64 z (cos.f64 y)) (+.f64 x (sin.f64 y))) (pow.f64 (+.f64 x (sin.f64 y)) 2)))
	0.2b	(fma.f64 (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
▶	0.2b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (*.f64 (cbrt.f64 (cos.f64 y)) z) (+.f64 x (sin.f64 y)))
	31.1b	(+.f64 (+.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))

Compiler

Compiled 2049 to 681 computations (66.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) z)
✓	0.3b	(pow.f64 (cos.f64 y) 2)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series190.0ms (4%)

Counts

4 → 52

Calls

15 calls:

30.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))	y	inf
26.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))	y	-inf
19.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) z)	y	-inf
19.0ms	(cbrt.f64 (cos.f64 y))	y	-inf
19.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) z)	y	inf

rewrite58.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`log1p-expm1-u_binary64`
656×	`expm1-log1p-u_binary64`
355×	`log-prod_binary64`
139×	`expm1-udef_binary64`
139×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	175	27
2	1906	27

Stop Event

1×	node limit

Counts

4 → 98

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

533×	`fma-neg_binary64`
500×	`sub-neg_binary64`
259×	`*-commutative_binary64`
234×	`distribute-rgt-neg-in_binary64`
230×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	487
1	169	475
2	499	466
3	1912	466
4	4776	466

Stop Event

1×	node limit

Counts

150 → 128

prune187.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	129	6	135

Error

Counts

135 → 6

Alt Table

Status	Error	Program
	0.6b	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) (+.f64 x (sin.f64 y)))
	42.3b	(/.f64 (+.f64 (pow.f64 (+.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (fma.f64 (.f64 z (cos.f64 y)) (-.f64 (*.f64 z (cos.f64 y)) (+.f64 x (sin.f64 y))) (pow.f64 (+.f64 x (sin.f64 y)) 2)))
▶	0.2b	(fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 4))) (*.f64 (cbrt.f64 (cos.f64 y)) z) (+.f64 x (sin.f64 y)))
	15.6b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (*.f64 (pow.f64 (pow.f64 (cos.f64 y) 1/6) 2) z) (+.f64 x (sin.f64 y)))

Compiler

Compiled 2811 to 1176 computations (58.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) z)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 4))
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.4b	(pow.f64 (cos.f64 y) 4)

series65.0ms (1.4%)

Counts

2 → 16

Calls

6 calls:

29.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 4))	y	-inf
27.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 4))	y	inf
5.0ms	(pow.f64 (cos.f64 y) 4)	y	-inf
2.0ms	(pow.f64 (cos.f64 y) 4)	y	inf
1.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 4))	y	0

rewrite37.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

455×	`log1p-expm1-u_binary64`
455×	`expm1-log1p-u_binary64`
313×	`unpow-prod-down_binary64`
224×	`log-prod_binary64`
137×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	122	14
2	1329	14

Stop Event

1×	node limit

Counts

2 → 73

simplify50.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

496×	`distribute-rgt-neg-in_binary64`
432×	`distribute-lft-neg-in_binary64`
409×	`fma-def_binary64`
396×	`associate-l_binary64`
341×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	176
1	95	168
2	249	160
3	809	156
4	3372	156

Stop Event

1×	node limit

Counts

89 → 87

prune160.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	149	6	155

Error

Counts

155 → 6

Alt Table

Status	Error	Program
▶	0.6b	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) (+.f64 x (sin.f64 y)))
	42.3b	(/.f64 (+.f64 (pow.f64 (+.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (fma.f64 (.f64 z (cos.f64 y)) (-.f64 (*.f64 z (cos.f64 y)) (+.f64 x (sin.f64 y))) (pow.f64 (+.f64 x (sin.f64 y)) 2)))
✓	0.2b	(fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 4))) (*.f64 (cbrt.f64 (cos.f64 y)) z) (+.f64 x (sin.f64 y)))
	15.6b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (*.f64 (pow.f64 (pow.f64 (cos.f64 y) 1/6) 2) z) (+.f64 x (sin.f64 y)))

Compiler

Compiled 3390 to 1517 computations (55.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2))
✓	0.2b	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.6b	(cbrt.f64 z)

series284.0ms (6%)

Counts

4 → 39

Calls

21 calls:

36.0ms	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))	y	inf
35.0ms	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))	y	-inf
30.0ms	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))	x	0
30.0ms	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))	x	-inf
22.0ms	(*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2))	y	inf

rewrite55.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

578×	`prod-diff_binary64`
246×	`fma-def_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
130×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	248	34
2	3061	32

Stop Event

1×	node limit

Counts

4 → 81

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-neg_binary64`
361×	`*-commutative_binary64`
306×	`distribute-rgt-neg-in_binary64`
303×	`distribute-lft-neg-in_binary64`
280×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	499
1	130	485
2	427	462
3	1920	455

Stop Event

1×	node limit

Counts

120 → 104

prune100.0ms (2.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	127	6	133

Error

Counts

133 → 6

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (+.f64 x (sin.f64 y)))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) (+.f64 x (sin.f64 y)))
	42.3b	(/.f64 (+.f64 (pow.f64 (+.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (fma.f64 (.f64 z (cos.f64 y)) (-.f64 (*.f64 z (cos.f64 y)) (+.f64 x (sin.f64 y))) (pow.f64 (+.f64 x (sin.f64 y)) 2)))
✓	0.2b	(fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 4))) (*.f64 (cbrt.f64 (cos.f64 y)) z) (+.f64 x (sin.f64 y)))
	15.6b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (*.f64 (pow.f64 (pow.f64 (cos.f64 y) 1/6) 2) z) (+.f64 x (sin.f64 y)))

Compiler

Compiled 2168 to 820 computations (62.2% saved)

regimes290.0ms (6.1%)

Accuracy

Total 0.0b remaining (55.2%)

Threshold costs 0.0b (55.2%)

Counts

68 → 1

Compiler

Compiled 4708 to 3118 computations (33.8% 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

Stop Event

1×

saturated

end104.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 143 to 87 computations (39.2% saved)

Details

analyze634.0ms (13.3%)

sample2.2s (46.6%)

preprocess20.0ms (0.4%)

simplify6.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series19.0ms (0.4%)

rewrite52.0ms (1.1%)

simplify40.0ms (0.8%)

prune74.0ms (1.6%)

localize15.0ms (0.3%)

series190.0ms (4%)

rewrite58.0ms (1.2%)

simplify41.0ms (0.9%)

prune187.0ms (3.9%)

localize14.0ms (0.3%)

series65.0ms (1.4%)

rewrite37.0ms (0.8%)

simplify50.0ms (1.1%)

prune160.0ms (3.3%)

localize12.0ms (0.3%)

series284.0ms (6%)

rewrite55.0ms (1.2%)

simplify29.0ms (0.6%)

prune100.0ms (2.1%)

regimes290.0ms (6.1%)

simplify2.0ms (0%)

end104.0ms (2.2%)

Profiling