Details

analyze431.0ms (10%)

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)

sample2.7s (63%)

Results

1.4s	2052×	body	1024	valid
711.0ms	4648×	body	128	valid
417.0ms	1053×	body	512	valid
139.0ms	495×	body	256	valid
13.0ms	8×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% 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 (0.2%)

Local error

Found 3 expressions with local error:

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

series21.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

14.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
1.0ms	(cos.f64 y)

rewrite43.0ms (1%)

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	21
1	156	21
2	1869	21

Stop Event

1×	node limit

Counts

3 → 56

Calls

3 calls:

42.0ms	(cos.f64 y)
42.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
42.0ms	(*.f64 z (sin.f64 y))

simplify41.0ms (1%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-neg_binary64`
359×	`sub-neg_binary64`
281×	`*-commutative_binary64`
270×	`unswap-sqr_binary64`
229×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	656
1	155	644
2	465	627
3	1691	625
4	4183	625

Stop Event

1×	node limit

Counts

120 → 81

prune58.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	7	82

Error

0.1b

Counts

82 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (.f64 z (sin.f64 y)))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	41.1b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	34.7b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	1.3b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))
	0.2b	(fma.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1255 to 516 computations (58.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series20.0ms (0.5%)

Counts

2 → 40

Calls

2 calls:

12.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
7.0ms	(*.f64 (cos.f64 y) x)

rewrite36.0ms (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

Calls

2 calls:

35.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
35.0ms	(*.f64 (cos.f64 y) x)

simplify35.0ms (0.8%)

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

prune61.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Error

0.1b

Counts

88 → 8

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (.f64 z (sin.f64 y)))
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	41.1b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	34.7b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	1.3b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))
▶	0.2b	(fma.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.0b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))

Compiler

Compiled 1260 to 548 computations (56.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(expm1.f64 (log1p.f64 (cos.f64 y)))
✓	0.3b	(log1p.f64 (cos.f64 y))

series155.0ms (3.6%)

Counts

3 → 60

Calls

3 calls:

139.0ms	(log1p.f64 (cos.f64 y))
13.0ms	(fma.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
3.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

rewrite46.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	177	20
2	2078	20

Stop Event

1×	node limit

Counts

3 → 60

Calls

3 calls:

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

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

652×	`distribute-rgt-neg-in_binary64`
372×	`sub-neg_binary64`
372×	`fma-neg_binary64`
262×	`*-commutative_binary64`
237×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	578
1	143	574
2	404	566
3	1518	564
4	3961	564

Stop Event

1×	node limit

Counts

120 → 87

prune75.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	110	8	118

Error

0.1b

Counts

118 → 8

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (.f64 z (sin.f64 y)))
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	41.1b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	34.7b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	1.3b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))
✓	0.2b	(fma.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.0b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))

Compiler

Compiled 1752 to 717 computations (59.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f64 (cos.f64 y))
✓	0.1b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.3b	(log.f64 (exp.f64 (cos.f64 y)))

series18.0ms (0.4%)

Counts

3 → 52

Calls

3 calls:

14.0ms	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
2.0ms	(exp.f64 (cos.f64 y))
2.0ms	(log.f64 (exp.f64 (cos.f64 y)))

rewrite42.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log1p-expm1-u_binary64`
751×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
82×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	179	20
2	2056	20

Stop Event

1×	node limit

Counts

3 → 62

Calls

3 calls:

41.0ms	(exp.f64 (cos.f64 y))
41.0ms	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
41.0ms	(log.f64 (exp.f64 (cos.f64 y)))

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
342×	`sub-neg_binary64`
321×	`*-commutative_binary64`
295×	`distribute-rgt-neg-in_binary64`
282×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	562
1	147	554
2	447	540
3	1736	531
4	4415	531

Stop Event

1×	node limit

Counts

114 → 88

prune79.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	111	8	119

Error

0.1b

Counts

119 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	41.1b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	34.7b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	1.3b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))
✓	0.2b	(fma.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.3b	(fma.f64 x (log.f64 (exp.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.3b	(fma.f64 x (log.f64 (pow.f64 (exp.f64 1) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.0b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))

Compiler

Compiled 1667 to 655 computations (60.7% saved)

regimes201.0ms (4.6%)

Accuracy

Total 0.1b remaining (43.3%)

Threshold costs 0.1b (43.3%)

Counts

52 → 1

Compiler

Compiled 3004 to 1962 computations (34.7% 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

end111.0ms (2.6%)

Compiler: Compiled 142 to 93 computations (34.5% saved)

Details

analyze431.0ms (10%)

sample2.7s (63%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series21.0ms (0.5%)

rewrite43.0ms (1%)

simplify41.0ms (1%)

prune58.0ms (1.3%)

localize7.0ms (0.2%)

series20.0ms (0.5%)

rewrite36.0ms (0.8%)

simplify35.0ms (0.8%)

prune61.0ms (1.4%)

localize10.0ms (0.2%)

series155.0ms (3.6%)

rewrite46.0ms (1.1%)

simplify39.0ms (0.9%)

prune75.0ms (1.7%)

localize10.0ms (0.2%)

series18.0ms (0.4%)

rewrite42.0ms (1%)

simplify42.0ms (1%)

prune79.0ms (1.8%)

regimes201.0ms (4.6%)

simplify2.0ms (0%)

end111.0ms (2.6%)

Profiling