Details

analyze553.0ms (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
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)

sample2.9s (50.7%)

Results

1.5s	1979×	body	1024	valid
796.0ms	4742×	body	128	valid
456.0ms	1041×	body	512	valid
138.0ms	489×	body	256	valid
7.0ms	5×	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

prune3.0ms (0%)

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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 y)
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.2b	(*.f64 z (cos.f64 y))

series22.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

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

rewrite46.0ms (0.8%)

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

3 → 59

Calls

3 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	156	21
2	1801	21
3	5105	21
0	0	0
1	0	0

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

689×	`distribute-rgt-neg-in_binary64`
583×	`distribute-lft-neg-in_binary64`
474×	`fma-neg_binary64`
354×	`sub-neg_binary64`
305×	`*-commutative_binary64`

Counts

123 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	644
1	132	637
2	372	620
3	1182	619
4	2838	619
5	4978	619
6	4984	619
7	4942	619

prune65.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	7	84

Error

0.1b

Counts

84 → 7

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
	41.6b	(cbrt.f64 (pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 3))
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (cos.f64 y) 1)))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	31.5b	(/.f64 (-.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (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 1305 to 544 computations (58.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 y)
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (cos.f64 y) 1)))
✓	0.2b	(*.f64 z (pow.f64 (cos.f64 y) 1))

series23.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (cos.f64 y) 1)))
8.0ms	(*.f64 z (pow.f64 (cos.f64 y) 1))

rewrite44.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

736×	`log1p-expm1-u_binary64`
736×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
154×	`log1p-udef_binary64`
87×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

43.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (cos.f64 y) 1)))
43.0ms	(*.f64 z (pow.f64 (cos.f64 y) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	176	18
2	1915	18
3	5148	18
0	0	0
1	0	0

simplify74.0ms (1.3%)

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

prune123.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Error

0.1b

Counts

90 → 7

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
	41.6b	(cbrt.f64 (pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 3))
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (cos.f64 y) 1)))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	31.5b	(/.f64 (-.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (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 1342 to 590 computations (56% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
✓	0.2b	(*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y))))
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 y)))
✓	0.3b	(log1p.f64 (cos.f64 y))

series166.0ms (2.9%)

Counts

4 → 84

Calls

4 calls:

142.0ms	(log1p.f64 (cos.f64 y))
15.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
7.0ms	(*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y))))
2.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

rewrite49.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 78

Calls

4 calls:

47.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
47.0ms	(*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y))))
47.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))
47.0ms	(log1p.f64 (cos.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	175	26
2	1994	26
3	5147	26
0	0	0
1	0	0

simplify122.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

882×	`distribute-rgt-neg-in_binary64`
589×	`fma-neg_binary64`
499×	`sub-neg_binary64`
389×	`*-commutative_binary64`
294×	`distribute-lft-neg-in_binary64`

Counts

162 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	768
1	171	761
2	477	742
3	1538	741
4	3621	741
5	4988	741

prune88.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	9	116

Error

0.1b

Counts

116 → 9

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
	41.6b	(cbrt.f64 (pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 3))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.3b	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 y))) 3))))
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (cos.f64 y) 1)))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))))
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 z (/.f64 (-.f64 (.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1)) 1) (+.f64 (+.f64 (cos.f64 y) 1) 1))))
	31.5b	(/.f64 (-.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (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 1787 to 813 computations (54.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1)) 1) (+.f64 (+.f64 (cos.f64 y) 1) 1))
✓	0.2b	(-.f64 (*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1)) 1)
✓	0.2b	(*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1))
✓	0.3b	(+.f64 (cos.f64 y) 1)

series23.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1)) 1) (+.f64 (+.f64 (cos.f64 y) 1) 1))
4.0ms	(*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1))
4.0ms	(-.f64 (*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1)) 1)
2.0ms	(+.f64 (cos.f64 y) 1)

rewrite144.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

882×	`prod-diff_binary64`
652×	`fma-udef_binary64`
352×	`fma-neg_binary64`
230×	`egg-rr`
159×	`expm1-udef_binary64`

Counts

4 → 230

Calls

4 calls:

140.0ms	(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1)) 1) (+.f64 (+.f64 (cos.f64 y) 1) 1))
140.0ms	(-.f64 (*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1)) 1)
140.0ms	(*.f64 (+.f64 (cos.f64 y) 1) (+.f64 (cos.f64 y) 1))
140.0ms	(+.f64 (cos.f64 y) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	47
1	217	28
2	2663	28
3	4781	28
4	4610	28
5	5071	28
0	0	0
1	0	0

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
502×	`distribute-rgt-neg-in_binary64`
441×	`distribute-lft-neg-in_binary64`
424×	`associate-l_binary64`
363×	`associate-r_binary64`

Counts

278 → 263

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	632
1	128	568
2	304	552
3	865	440
4	2905	416
5	4870	416
6	5047	416

prune494.0ms (8.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	384	3	387
Fresh	2	4	6
Picked	1	0	1
Done	1	1	2
Total	388	8	396

Error

0.1b

Counts

396 → 8

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (cos.f64 y)))))
	41.6b	(cbrt.f64 (pow.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))) 3))
	0.2b	(fma.f64 x (sin.f64 y) (.f64 z (.f64 (+.f64 (cos.f64 y) 2) (*.f64 (cos.f64 y) (/.f64 1 (+.f64 (cos.f64 y) 2))))))
	0.3b	(fma.f64 x (sin.f64 y) (*.f64 z (/.f64 (-.f64 (log.f64 (exp.f64 (pow.f64 (+.f64 (cos.f64 y) 1) 2))) 1) (+.f64 (+.f64 (cos.f64 y) 1) 1))))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	0.2b	(fma.f64 x (sin.f64 y) (.f64 z (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 y)) 2)) 3) (pow.f64 (+.f64 (cos.f64 y) 2) 3)))))
	31.5b	(/.f64 (-.f64 (.f64 (.f64 x (sin.f64 y)) (.f64 x (sin.f64 y))) (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 11116 to 6809 computations (38.7% saved)

regimes399.0ms (7%)

Accuracy

Total 0.1b remaining (50.2%)

Threshold costs 0.1b (50.2%)

Counts

97 → 1

Compiler

Compiled 6732 to 4694 computations (30.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	17	36
2	17	36

end141.0ms (2.5%)

Compiler: Compiled 218 to 139 computations (36.2% saved)

Details

analyze553.0ms (9.7%)

sample2.9s (50.7%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series22.0ms (0.4%)

rewrite46.0ms (0.8%)

simplify95.0ms (1.7%)

prune65.0ms (1.1%)

localize8.0ms (0.1%)

series23.0ms (0.4%)

rewrite44.0ms (0.8%)

simplify74.0ms (1.3%)

prune123.0ms (2.2%)

localize12.0ms (0.2%)

series166.0ms (2.9%)

rewrite49.0ms (0.9%)

simplify122.0ms (2.1%)

prune88.0ms (1.5%)

localize14.0ms (0.2%)

series23.0ms (0.4%)

rewrite144.0ms (2.5%)

simplify77.0ms (1.3%)

prune494.0ms (8.7%)

regimes399.0ms (7%)

simplify2.0ms (0%)

end141.0ms (2.5%)

Profiling