Details

analyze503.0ms (8.9%)

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)

sample3.3s (58.5%)

Results

1.8s	2056×	body	1024	valid
884.0ms	4702×	body	128	valid
395.0ms	1000×	body	512	valid
190.0ms	488×	body	256	valid
14.0ms	10×	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`

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(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)))
✓	0.2b	(*.f64 z (cos.f64 y))

series23.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
6.0ms	(*.f64 z (cos.f64 y))

rewrite42.0ms (0.7%)

Algorithm

1×	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 → 40

Calls

2 calls:

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

simplify71.0ms (1.2%)

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

100 → 57

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

prune43.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	50	7	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	7	58

Error

0.1b

Counts

58 → 7

Alt Table

Status	Error	Program
▶	0.2b	(pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 1)
	0.2b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	24.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	24.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
	32.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
	38.9b	(/.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))))))
	1.4b	(.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 994 to 403 computations (59.5% saved)

localize8.0ms (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)))
	0.2b	(*.f64 z (cos.f64 y))

prune44.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Error

0.1b

Counts

64 → 7

Alt Table

Status	Error	Program
✓	0.2b	(pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 1)
▶	0.2b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	24.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	24.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
	32.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
	38.9b	(/.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))))))
	1.4b	(.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 1095 to 508 computations (53.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

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

rewrite49.0ms (0.9%)

Algorithm

1×	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 → 40

Calls

2 calls:

48.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
48.0ms	(*.f64 (sin.f64 y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1801	18
3	5105	18

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
602×	`distribute-rgt-neg-in_binary64`
555×	`distribute-lft-neg-in_binary64`
523×	`associate-l_binary64`
430×	`associate-r_binary64`

Counts

80 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	480
1	117	472
2	328	460
3	963	451
4	3204	451
5	4809	451
6	5026	451

prune43.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	58	7	65

Error

0.1b

Counts

65 → 7

Alt Table

Status	Error	Program
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))))
	24.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
✓	0.2b	(pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 1)
✓	0.2b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	24.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
	32.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
▶	1.4b	(.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 912 to 374 computations (59% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 z (cos.f64 y))
✓	0.3b	(.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))
✓	0.6b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
✓	0.6b	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

series584.0ms (10.3%)

Counts

3 → 108

Calls

3 calls:

297.0ms

(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)

270.0ms

(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

16.0ms

(*.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))

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`log1p-expm1-u_binary64`
879×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
107×	`add-sqr-sqrt_binary64`
99×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

52.0ms

(*.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))

52.0ms

(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)

52.0ms

(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	219	43
2	2312	43
3	5746	43

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

550×	`associate-r_binary64`
501×	`times-frac_binary64`
386×	`associate-l_binary64`
330×	`associate-/l*_binary64`
322×	`associate-/r*_binary64`

Counts

170 → 185

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	361	4788
1	1329	4657
2	5446	4657

prune231.0ms (4.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	307	6	313
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	308	12	320

Error

0.0b

Counts

320 → 12

Alt Table

Status	Error	Program
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))))
	24.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	43.4b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (.f64 (pow.f64 (cos.f64 y) 2) (.f64 z z))))
✓	0.2b	(pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 1)
✓	0.2b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
✓	1.4b	(.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))
	1.8b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 3) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	32.4b	(fma.f64 x (sin.f64 y) (pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2))
	14.6b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 4)))
	33.2b	(.f64 (exp.f64 (log.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))
	2.2b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) 3) 2))
	14.9b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) 2))) 2))

Compiler

Compiled 13285 to 5938 computations (55.3% saved)

regimes256.0ms (4.5%)

Accuracy

Total 0.1b remaining (46.8%)

Threshold costs 0.1b (46.8%)

Counts

60 → 1

Compiler

Compiled 4156 to 2522 computations (39.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	13	12
2	12	12

end184.0ms (3.2%)

Compiler: Compiled 285 to 162 computations (43.2% saved)

Details

analyze503.0ms (8.9%)

sample3.3s (58.5%)

simplify6.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite42.0ms (0.7%)

simplify71.0ms (1.2%)

prune43.0ms (0.8%)

localize8.0ms (0.1%)

prune44.0ms (0.8%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite49.0ms (0.9%)

simplify81.0ms (1.4%)

prune43.0ms (0.8%)

localize10.0ms (0.2%)

series584.0ms (10.3%)

rewrite54.0ms (0.9%)

simplify81.0ms (1.4%)

prune231.0ms (4.1%)

regimes256.0ms (4.5%)

simplify2.0ms (0%)

end184.0ms (3.2%)

Profiling