Details

analyze486.0ms (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
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)

sample3.0s (42.7%)

Results

1.4s	2093×	body	1024	valid
867.0ms	4611×	body	128	valid
420.0ms	1046×	body	512	valid
153.0ms	497×	body	256	valid
12.0ms	9×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (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

prune4.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(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 2 expressions with local error:

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

series22.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

14.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
7.0ms	(*.f64 z (cos.f64 y))

rewrite48.0ms (0.7%)

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

2 → 38

Calls

2 calls:

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

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

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

802×	`distribute-rgt-neg-in_binary64`
744×	`cancel-sign-sub-inv_binary64`
698×	`fma-def_binary64`
621×	`distribute-lft-neg-in_binary64`
362×	`fma-neg_binary64`

Counts

98 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	588
1	106	587
2	305	576
3	987	568
4	3070	568
5	4686	568
6	5000	568

prune39.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	6	56

Error

0.1b

Counts

56 → 6

Alt Table

Status	Error	Program
	25.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	30.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
▶	0.8b	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))
	40.7b	(/.f64 (+.f64 (pow.f64 (.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (+.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (-.f64 (pow.f64 (.f64 z (cos.f64 y)) 2) (.f64 (.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))))))
	1.3b	(.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))

Compiler

Compiled 941 to 378 computations (59.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))
	0.1b	(*.f64 z (cos.f64 y))
✓	0.6b	(cbrt.f64 (*.f64 z (cos.f64 y)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)

series1.4s (20.5%)

Counts

3 → 84

Calls

3 calls:

518.0ms	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))
494.0ms	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
414.0ms	(cbrt.f64 (*.f64 z (cos.f64 y)))

rewrite56.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

863×	`log1p-expm1-u_binary64`
863×	`expm1-log1p-u_binary64`
297×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`

Counts

3 → 82

Calls

3 calls:

54.0ms	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))
54.0ms	(cbrt.f64 (*.f64 z (cos.f64 y)))
54.0ms	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	205	26
2	2263	26
3	5836	26
0	0	0
1	0	0

simplify120.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-neg_binary64`
495×	`distribute-rgt-neg-in_binary64`
480×	`distribute-lft-neg-in_binary64`
304×	`unswap-sqr_binary64`
296×	`associate-r_binary64`

Counts

166 → 120

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	82	1368
1	236	1361
2	643	1197
3	2301	897
4	4948	885
5	4968	885
6	5000	885
7	4931	885

prune105.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	141	8	149

Error

0.1b

Counts

149 → 8

Alt Table

Status	Error	Program
	18.7b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cos.f64 y) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z)))
	40.7b	(/.f64 (+.f64 (pow.f64 (.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (+.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (-.f64 (pow.f64 (.f64 z (cos.f64 y)) 2) (.f64 (.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))))))
	0.9b	(fma.f64 x (sin.f64 y) (pow.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 (cos.f64 y))) 3))
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z)))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	30.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
✓	0.8b	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))
	16.4b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) z)))

Compiler

Compiled 2421 to 1049 computations (56.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) z)
✓	0.2b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z))
✓	0.2b	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
✓	0.3b	(cbrt.f64 (cos.f64 y))

series737.0ms (10.6%)

Counts

4 → 72

Calls

4 calls:

395.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) z)
168.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
165.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z))

rewrite81.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

708×	`log1p-expm1-u_binary64`
708×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`

Counts

4 → 72

Calls

4 calls:

80.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) z)
80.0ms	(.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z))
80.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
80.0ms	(cbrt.f64 (cos.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	178	25
2	1887	25
3	4965	25
4	4915	25
0	0	0
1	0	0

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

736×	`distribute-rgt-neg-in_binary64`
634×	`fma-neg_binary64`
537×	`sub-neg_binary64`
399×	`neg-mul-1_binary64`
385×	`*-commutative_binary64`

Counts

144 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	628
1	187	621
2	541	604
3	1721	602
4	3700	602
5	4861	602
6	5026	602

prune121.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	134	8	142

Error

0.1b

Counts

142 → 8

Alt Table

Status	Error	Program
	30.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
▶	0.2b	(fma.f64 x (sin.f64 y) (.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) z)))
✓	0.8b	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))
	16.4b	(fma.f64 x (sin.f64 y) (.f64 (pow.f64 (pow.f64 (cos.f64 y) 1/3) 2) (.f64 (cbrt.f64 (cos.f64 y)) z)))
	18.7b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cos.f64 y) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z)))
	40.7b	(/.f64 (+.f64 (pow.f64 (.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (+.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (-.f64 (pow.f64 (.f64 z (cos.f64 y)) 2) (.f64 (.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	0.9b	(fma.f64 x (sin.f64 y) (pow.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 (cos.f64 y))) 3))

Compiler

Compiled 2739 to 1240 computations (54.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) z)
✓	0.2b	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) z))
✓	0.3b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series12.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

7.0ms	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) z))
5.0ms	(pow.f64 (cos.f64 y) 2)

rewrite48.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`
95×	`add-cube-cbrt_binary64`
95×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

47.0ms	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) z))
47.0ms	(pow.f64 (cos.f64 y) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	224	12
2	2238	12
3	5106	12
0	0	0
1	0	0

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

642×	`distribute-rgt-neg-in_binary64`
636×	`associate-l_binary64`
620×	`distribute-lft-neg-in_binary64`
545×	`fma-def_binary64`
378×	`cancel-sign-sub-inv_binary64`

Counts

65 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	239
1	92	232
2	262	224
3	790	218
4	2703	218
5	4654	218
6	5093	218

prune101.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	107	8	115

Error

0.1b

Counts

115 → 8

Alt Table

Status	Error	Program
	30.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
✓	0.2b	(fma.f64 x (sin.f64 y) (.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) z)))
✓	0.8b	(fma.f64 x (sin.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))
	16.4b	(fma.f64 x (sin.f64 y) (.f64 (pow.f64 (pow.f64 (cos.f64 y) 1/3) 2) (.f64 (cbrt.f64 (cos.f64 y)) z)))
	18.7b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cos.f64 y) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z)))
	40.7b	(/.f64 (+.f64 (pow.f64 (.f64 x (sin.f64 y)) 3) (pow.f64 (.f64 z (cos.f64 y)) 3)) (+.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (-.f64 (pow.f64 (.f64 z (cos.f64 y)) 2) (.f64 (.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	0.9b	(fma.f64 x (sin.f64 y) (pow.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 (cos.f64 y))) 3))

Compiler

Compiled 2170 to 1093 computations (49.6% saved)

regimes182.0ms (2.6%)

Accuracy

Total 0.1b remaining (39.8%)

Threshold costs 0.1b (39.8%)

Counts

46 → 1

Compiler

Compiled 2888 to 1870 computations (35.2% saved)

simplify4.0ms (0.1%)

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

end128.0ms (1.8%)

Compiler: Compiled 174 to 108 computations (37.9% saved)

Details

analyze486.0ms (7%)

sample3.0s (42.7%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series22.0ms (0.3%)

rewrite48.0ms (0.7%)

simplify75.0ms (1.1%)

prune39.0ms (0.6%)

localize12.0ms (0.2%)

series1.4s (20.5%)

rewrite56.0ms (0.8%)

simplify120.0ms (1.7%)

prune105.0ms (1.5%)

localize10.0ms (0.1%)

series737.0ms (10.6%)

rewrite81.0ms (1.2%)

simplify83.0ms (1.2%)

prune121.0ms (1.7%)

localize12.0ms (0.2%)

series12.0ms (0.2%)

rewrite48.0ms (0.7%)

simplify64.0ms (0.9%)

prune101.0ms (1.4%)

regimes182.0ms (2.6%)

simplify4.0ms (0.1%)

end128.0ms (1.8%)

Profiling