Details

analyze442.0ms (8.7%)

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)

sample2.8s (54.4%)

Results

1.4s	2036×	body	1024	valid
738.0ms	4615×	body	128	valid
427.0ms	1052×	body	512	valid
151.0ms	550×	body	256	valid
8.0ms	3×	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

0.1b

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 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))

series23.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

13.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
8.0ms	(*.f64 z (sin.f64 y))
2.0ms	(cos.f64 y)

rewrite9.0ms (0.2%)

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:

7.0ms	(*.f64 z (sin.f64 y))
1.0ms	(cos.f64 y)
0.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify90.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
495×	`sub-neg_binary64`
289×	`associate-l_binary64`
258×	`unswap-sqr_binary64`
256×	`distribute-rgt-neg-in_binary64`

Counts

103 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1088
1	229	1018
2	653	1001
3	1805	999
4	3991	999
5	4797	999
6	4959	999

prune78.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Error

0.0b

Counts

83 → 12

Alt Table

Status	Error	Program
	32.4b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.2b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	23.7b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.2b	(fma.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	32.5b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.2b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	41.2b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1551 to 586 computations (62.2% 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 (sin.f64 y) z (*.f64 (cos.f64 y) x))
✓	0.1b	(*.f64 (cos.f64 y) x)

series21.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

13.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
8.0ms	(*.f64 (cos.f64 y) x)

rewrite4.0ms (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:

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

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

803×	`distribute-rgt-neg-in_binary64`
796×	`fma-def_binary64`
741×	`cancel-sign-sub-inv_binary64`
379×	`fma-neg_binary64`
324×	`*-commutative_binary64`

Counts

70 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	840
1	173	788
2	484	778
3	1314	771
4	3692	771
5	4945	771

prune87.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	81	13	94

Error

0.0b

Counts

94 → 13

Alt Table

Status	Error	Program
	32.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	0.2b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
	32.4b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	23.7b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	32.5b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.2b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	28.9b	(fma.f64 (sin.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)) (.f64 (*.f64 x x) x))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
▶	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) x))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1551 to 619 computations (60.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series228.0ms (4.5%)

Counts

4 → 84

Calls

4 calls:

204.0ms	(log1p.f64 (cos.f64 y))
15.0ms	(fma.f64 (sin.f64 y) z (*.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) x))
7.0ms	(*.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) x)
2.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

2.0ms	(*.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) x)
0.0ms	(log1p.f64 (cos.f64 y))
0.0ms	(fma.f64 (sin.f64 y) z (*.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) x))
0.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
303×	`distribute-rgt-neg-in_binary64`
295×	`distribute-lft-neg-in_binary64`
279×	`associate-l_binary64`
240×	`associate-r_binary64`

Counts

136 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1291
1	248	1215
2	672	1197
3	1884	1195
4	4811	1195
5	4956	1195

prune112.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Error

0.0b

Counts

126 → 12

Alt Table

Status	Error	Program
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
▶	0.2b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
	32.4b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	23.7b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	32.5b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.2b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	32.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) (sqrt.f64 x)) (sqrt.f64 x)))
	16.1b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (cos.f64 y)))) (.f64 x (sqrt.f64 (cos.f64 y)))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2094 to 791 computations (62.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
✓	0.3b	(*.f64 (cos.f64 y) (cos.f64 y))
✓	0.3b	(cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))

series12.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
5.0ms	(*.f64 (cos.f64 y) (cos.f64 y))
2.0ms	(cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 74

Calls

3 calls:

5.0ms	(.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
4.0ms	(cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))
3.0ms	(*.f64 (cos.f64 y) (cos.f64 y))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
612×	`unswap-sqr_binary64`
392×	`associate-l_binary64`
328×	`cancel-sign-sub-inv_binary64`
312×	`associate-r_binary64`

Counts

110 → 115

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	942
1	216	775
2	570	763
3	1738	714
4	3804	668
5	4646	668
6	4915	668

prune170.0ms (3.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	152	12	164

Error

0.0b

Counts

164 → 12

Alt Table

Status	Error	Program
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
	32.4b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	0.2b	(fma.f64 x (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 6)) (cos.f64 y))) (.f64 z (sin.f64 y)))
	23.7b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	32.5b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.2b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	32.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (expm1.f64 (log1p.f64 (cos.f64 y))) (sqrt.f64 x)) (sqrt.f64 x)))
	16.1b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (cos.f64 y)))) (.f64 x (sqrt.f64 (cos.f64 y)))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	31.6b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 3108 to 984 computations (68.3% saved)

regimes585.0ms (11.5%)

Accuracy

Total 0.1b remaining (66.9%)

Threshold costs 0.1b (66.9%)

Counts

116 → 1

Compiler

Compiled 6960 to 4402 computations (36.8% 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

end167.0ms (3.3%)

Compiler: Compiled 244 to 138 computations (43.4% saved)

Details

analyze442.0ms (8.7%)

sample2.8s (54.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite9.0ms (0.2%)

simplify90.0ms (1.8%)

prune78.0ms (1.5%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify66.0ms (1.3%)

prune87.0ms (1.7%)

localize11.0ms (0.2%)

series228.0ms (4.5%)

rewrite5.0ms (0.1%)

simplify80.0ms (1.6%)

prune112.0ms (2.2%)

localize10.0ms (0.2%)

series12.0ms (0.2%)

rewrite14.0ms (0.3%)

simplify86.0ms (1.7%)

prune170.0ms (3.3%)

regimes585.0ms (11.5%)

simplify2.0ms (0%)

end167.0ms (3.3%)

Profiling