Details

analyze461.0ms (9.7%)

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
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)

sample2.9s (59.9%)

Results

1.5s	2175×	body	1024	valid
740.0ms	4538×	body	128	valid
414.0ms	1020×	body	512	valid
153.0ms	521×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess19.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def_binary64`
8×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	38	48
2	50	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

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

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

0.1b

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)

localize7.0ms (0.1%)

Local error

Found 2 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))

series24.0ms (0.5%)

Counts

2 → 60

Calls

15 calls:

5.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))	z	0
2.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))	z	inf
2.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))	z	-inf
2.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))	x	-inf
2.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))	x	inf

rewrite39.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
147×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1869	18

Stop Event

1×	node limit

Counts

2 → 38

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

609×	`distribute-rgt-neg-in_binary64`
502×	`associate-l_binary64`
420×	`fma-neg_binary64`
410×	`associate-r_binary64`
226×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	600
1	117	592
2	353	580
3	1244	579
4	3964	579

Stop Event

1×	node limit

Counts

98 → 56

prune37.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Error

0.1b

Counts

57 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	1.4b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	36.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	29.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	40.8b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	18.7b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 982 to 396 computations (59.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.4%)

Counts

2 → 40

Calls

15 calls:

2.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))	y	0
2.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))	z	inf
2.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))	x	-inf
2.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))	z	0
2.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))	z	-inf

rewrite37.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
147×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1869	18

Stop Event

1×	node limit

Counts

2 → 38

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

739×	`cancel-sign-sub-inv_binary64`
698×	`fma-def_binary64`
361×	`fma-neg_binary64`
271×	`sub-neg_binary64`
240×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	468
1	107	467
2	324	457
3	1258	450
4	4705	450

Stop Event

1×	node limit

Counts

78 → 56

prune41.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	57	6	63

Error

0.1b

Counts

63 → 6

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))
	36.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	29.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	40.8b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	18.7b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 943 to 376 computations (60.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series256.0ms (5.4%)

Counts

3 → 51

Calls

21 calls:

27.0ms	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))	y	-inf
26.0ms	(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)	y	-inf
26.0ms	(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)	y	inf
26.0ms	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))	y	inf
23.0ms	(cbrt.f64 (*.f64 (cos.f64 y) x))	y	-inf

rewrite51.0ms (1.1%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	219	26
2	2388	26

Stop Event

1×	node limit

Counts

3 → 82

simplify33.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
471×	`distribute-rgt-neg-in_binary64`
468×	`distribute-lft-neg-in_binary64`
278×	`associate-r_binary64`
260×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	562
1	163	555
2	532	536
3	2452	531

Stop Event

1×	node limit

Counts

133 → 107

prune95.0ms (2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	125	10	135

Error

0.1b

Counts

135 → 10

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x)))
✓	0.9b	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))
	36.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	29.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	40.8b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	29.4b	(.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) (cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 2)))
	18.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 2)))) (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
	36.2b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))))

Compiler

Compiled 2355 to 1031 computations (56.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series180.0ms (3.8%)

Counts

4 → 72

Calls

18 calls:

20.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)	y	-inf
20.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)	y	inf
20.0ms	(cbrt.f64 (cos.f64 y))	y	-inf
20.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)	y	-inf
19.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)	x	0

rewrite46.0ms (1%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	179	27
2	2038	27

Stop Event

1×	node limit

Counts

4 → 72

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
275×	`distribute-rgt-neg-in_binary64`
270×	`distribute-lft-neg-in_binary64`
252×	`fma-def_binary64`
226×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	628
1	187	621
2	572	604
3	2237	602

Stop Event

1×	node limit

Counts

144 → 103

prune137.0ms (2.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	135	9	144

Error

0.1b

Counts

144 → 9

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x)))
✓	0.9b	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))
	0.3b	(fma.f64 (sin.f64 y) z (.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) x)))
	36.3b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	29.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	29.4b	(.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) (cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 2)))
	18.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 2)))) (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))

Compiler

Compiled 2658 to 1170 computations (56% saved)

regimes154.0ms (3.2%)

Accuracy

Total 0.1b remaining (51.8%)

Threshold costs 0.1b (51.8%)

Counts

41 → 1

Compiler

Compiled 2560 to 1570 computations (38.7% 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

end126.0ms (2.6%)

Stop Event

1×

fuel

Compiler

Compiled 197 to 118 computations (40.1% saved)

Details

analyze461.0ms (9.7%)

sample2.9s (59.9%)

preprocess19.0ms (0.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series24.0ms (0.5%)

rewrite39.0ms (0.8%)

simplify42.0ms (0.9%)

prune37.0ms (0.8%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite37.0ms (0.8%)

simplify36.0ms (0.7%)

prune41.0ms (0.9%)

localize9.0ms (0.2%)

series256.0ms (5.4%)

rewrite51.0ms (1.1%)

simplify33.0ms (0.7%)

prune95.0ms (2%)

localize10.0ms (0.2%)

series180.0ms (3.8%)

rewrite46.0ms (1%)

simplify34.0ms (0.7%)

prune137.0ms (2.9%)

regimes154.0ms (3.2%)

simplify2.0ms (0%)

end126.0ms (2.6%)

Profiling