Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.4s (59.8%)

Infinites

0% of outputs are infinite.

Results

1.8s	2070×	body	1024	valid
844.0ms	4600×	body	128	valid
494.0ms	1046×	body	512	valid
174.0ms	537×	body	256	valid
6.0ms	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%)

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)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series22.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

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

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

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
465×	`distribute-rgt-neg-in_binary64`
379×	`distribute-lft-neg-in_binary64`
307×	`distribute-rgt-in_binary64`
280×	`*-commutative_binary64`

Counts

90 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	972
1	183	913
2	538	901
3	1443	900
4	2915	900
5	4952	900
6	5012	900

prune46.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	6	66

Error

0.1b

Counts

66 → 6

Alt Table

Status	Error	Program
	34.7b	(.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)))))
	23.3b	(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)))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.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)))))
	38.4b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))

Compiler

Compiled 1096 to 373 computations (66% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series22.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
7.0ms	(*.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))

simplify61.0ms (1.1%)

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

prune47.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Error

0.0b

Counts

71 → 8

Alt Table

Status	Error	Program
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	23.3b	(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)))))
	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)))))
	32.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	18.8b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
▶	0.4b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))
	33.2b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (*.f64 (cos.f64 y) x))))

Compiler

Compiled 1163 to 412 computations (64.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series808.0ms (14.3%)

Counts

4 → 72

Calls

4 calls:

419.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
216.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
165.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
4.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
2.0ms	(cbrt.f64 (cos.f64 y))

simplify115.0ms (2%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-neg_binary64`
389×	`cancel-sign-sub-inv_binary64`
381×	`*-commutative_binary64`
267×	`fma-def_binary64`
221×	`associate-+l+_binary64`

Counts

175 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	1804
1	339	1606
2	1140	1555
3	2286	1535
4	4798	1409
5	4941	1409
6	4947	1409

prune168.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Error

0.0b

Counts

212 → 8

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x)))
	23.3b	(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)))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.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)))))
	32.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	18.8b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	0.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))
	0.3b	(fma.f64 (sin.f64 y) z (.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) x)))

Compiler

Compiled 4835 to 1322 computations (72.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) x)
✓	0.2b	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))
✓	0.2b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series11.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

7.0ms	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
15×	`prod-exp_binary64`
14×	`unpow-prod-down_binary64`
12×	`associate-l_binary64`
9×	`pow-exp_binary64`

Counts

2 → 57

Calls

2 calls:

6.0ms	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify128.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-neg_binary64`
490×	`sqr-pow_binary64`
456×	`fma-def_binary64`
433×	`*-commutative_binary64`
298×	`cancel-sign-sub-inv_binary64`

Counts

85 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1237
1	278	951
2	831	813
3	1736	809
4	3579	674
5	4060	674
6	4764	674
7	4980	674
8	4885	674

prune164.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	150	8	158

Error

0.0b

Counts

158 → 8

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x)))
	23.3b	(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)))))
	0.3b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (cbrt.f64 (pow.f64 (cos.f64 y) 2))) 1/3) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))))
	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))))
	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)))))
	26.5b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (cbrt.f64 (.f64 (cos.f64 y) (pow.f64 x 3)))))
	18.8b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))

Compiler

Compiled 3348 to 1568 computations (53.2% saved)

regimes364.0ms (6.4%)

Accuracy

Total 0.1b remaining (55.6%)

Threshold costs 0.1b (55.6%)

Counts

91 → 1

Compiler

Compiled 6180 to 3790 computations (38.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end134.0ms (2.4%)

Compiler: Compiled 199 to 116 computations (41.7% saved)

Details

analyze4.0ms (0.1%)

sample3.4s (59.8%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series22.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify84.0ms (1.5%)

prune46.0ms (0.8%)

localize7.0ms (0.1%)

series22.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify61.0ms (1.1%)

prune47.0ms (0.8%)

localize10.0ms (0.2%)

series808.0ms (14.3%)

rewrite23.0ms (0.4%)

simplify115.0ms (2%)

prune168.0ms (3%)

localize13.0ms (0.2%)

series11.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify128.0ms (2.3%)

prune164.0ms (2.9%)

regimes364.0ms (6.4%)

simplify4.0ms (0.1%)

end134.0ms (2.4%)

Profiling