Details

analyze611.0ms (11.9%)

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)

sample2.9s (56.3%)

Results

1.5s	2117×	body	1024	valid
744.0ms	4606×	body	128	valid
443.0ms	1046×	body	512	valid
147.0ms	483×	body	256	valid
6.0ms	4×	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

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

0.2b

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 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))

series24.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

14.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
8.0ms	(*.f64 z (cos.f64 y))
2.0ms	(cos.f64 y)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 39

Calls

3 calls:

3.0ms	(*.f64 z (cos.f64 y))
2.0ms	(cos.f64 y)
0.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

738×	`distribute-rgt-neg-in_binary64`
593×	`fma-neg_binary64`
367×	`*-commutative_binary64`
354×	`sub-neg_binary64`
331×	`neg-mul-1_binary64`

Counts

103 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1076
1	200	1011
2	592	993
3	1661	993
4	3588	993
5	4917	993
6	5070	993

prune58.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Error

0.0b

Counts

82 → 9

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
▶	0.2b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	35.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	33.8b	(fma.f64 y x (fma.f64 z (fma.f64 (.f64 y y) -1/2 1) (.f64 x (*.f64 (pow.f64 y 3) -1/6))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	33.3b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1415 to 541 computations (61.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 y)
✓	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)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(*.f64 (sin.f64 y) x)
0.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-neg_binary64`
405×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
293×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`

Counts

70 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	852
1	184	793
2	507	781
3	1282	780
4	2630	780
5	4874	780
6	4926	780

prune85.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Error

0.0b

Counts

92 → 11

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	35.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) x)) (cbrt.f64 (.f64 (sin.f64 y) x))) (cbrt.f64 (*.f64 (sin.f64 y) x))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.9b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	31.2b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))

Compiler

Compiled 1515 to 573 computations (62.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	0.1b	(*.f64 (sin.f64 y) x)
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series20.0ms (0.4%)

Counts

3 → 60

Calls

3 calls:

15.0ms	(fma.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
3.0ms	(expm1.f64 (cos.f64 y))
2.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log1p-expm1-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms	(expm1.f64 (cos.f64 y))
0.0ms	(fma.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

simplify106.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
550×	`sub-neg_binary64`
408×	`*-commutative_binary64`
281×	`distribute-rgt-neg-in_binary64`
275×	`distribute-lft-neg-in_binary64`

Counts

92 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	930
1	191	879
2	524	865
3	1655	858
4	4186	858
5	4727	858
6	4998	858
7	4899	858

prune100.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Error

0.0b

Counts

121 → 11

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	35.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) x)) (cbrt.f64 (.f64 (sin.f64 y) x))) (cbrt.f64 (*.f64 (sin.f64 y) x))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.9b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	31.2b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))

Compiler

Compiled 2043 to 726 computations (64.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
✓	0.2b	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
✓	0.4b	(pow.f64 (cos.f64 y) 3)

series31.0ms (0.6%)

Counts

4 → 76

Calls

4 calls:

15.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
7.0ms	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
7.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 94

Calls

4 calls:

6.0ms	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
2.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
0.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))

simplify113.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

366×	`fma-neg_binary64`
350×	`sub-neg_binary64`
344×	`sqr-pow_binary64`
343×	`*-commutative_binary64`
336×	`cancel-sign-sub-inv_binary64`

Counts

170 → 153

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	148	1661
1	298	1562
2	990	1524
3	2095	1524
4	3978	1521
5	4818	1521
6	4898	1521

prune195.0ms (3.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	152	12	164

Error

0.0b

Counts

164 → 12

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) z (*.f64 (sin.f64 y) x))
	35.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.9b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cbrt.f64 (pow.f64 (cos.f64 y) 3)))))
	26.8b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (*.f64 z z) z) (pow.f64 (cos.f64 y) 3))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) z)) (cbrt.f64 (.f64 (cos.f64 y) z))) (cbrt.f64 (*.f64 (cos.f64 y) z))))
	31.2b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	24.6b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) x)) (cbrt.f64 (.f64 (sin.f64 y) x))) (cbrt.f64 (*.f64 (sin.f64 y) x))))

Compiler

Compiled 2646 to 1294 computations (51.1% saved)

regimes473.0ms (9.2%)

Accuracy

Total 0.1b remaining (61.8%)

Threshold costs 0.1b (61.8%)

Counts

104 → 1

Compiler

Compiled 6296 to 3906 computations (38% 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

end158.0ms (3.1%)

Compiler: Compiled 244 to 137 computations (43.9% saved)

Details

analyze611.0ms (11.9%)

sample2.9s (56.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series24.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify95.0ms (1.9%)

prune58.0ms (1.1%)

localize9.0ms (0.2%)

series21.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify76.0ms (1.5%)

prune85.0ms (1.7%)

localize11.0ms (0.2%)

series20.0ms (0.4%)

rewrite2.0ms (0%)

simplify106.0ms (2.1%)

prune100.0ms (1.9%)

localize10.0ms (0.2%)

series31.0ms (0.6%)

rewrite13.0ms (0.3%)

simplify113.0ms (2.2%)

prune195.0ms (3.8%)

regimes473.0ms (9.2%)

simplify2.0ms (0%)

end158.0ms (3.1%)

Profiling