Details

analyze493.0ms (11.3%)

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)

sample3.0s (70%)

Results

1.6s	2158×	body	1024	valid
792.0ms	4536×	body	128	valid
458.0ms	1043×	body	512	valid
167.0ms	513×	body	256	valid
10.0ms	6×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess19.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def_binary64`
8×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	38	48
2	50	48
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 y (cos.f64 x)) (.f64 z (sin.f64 x)))
(+.f64 (.f64 z (cos.f64 y)) (.f64 x (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 z)) (.f64 y (sin.f64 z)))

Outputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 y (cos.f64 x)) (.f64 z (sin.f64 x)))
(fma.f64 y (cos.f64 x) (*.f64 z (sin.f64 x)))
(+.f64 (.f64 z (cos.f64 y)) (.f64 x (sin.f64 y)))
(fma.f64 z (cos.f64 y) (*.f64 x (sin.f64 y)))
(fma.f64 x (sin.f64 y) (*.f64 (cos.f64 y) z))
(+.f64 (.f64 x (cos.f64 z)) (.f64 y (sin.f64 z)))
(fma.f64 x (cos.f64 z) (*.f64 y (sin.f64 z)))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Outputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

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)

localize8.0ms (0.2%)

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))

series10.0ms (0.2%)

Counts

2 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(*.f64 z (sin.f64 y))
1.0ms	y	@	0	(*.f64 z (sin.f64 y))
1.0ms	x	@	-inf	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
1.0ms	x	@	0	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
1.0ms	z	@	inf	(*.f64 z (sin.f64 y))

rewrite40.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`pow1_binary64`
689×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
81×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1853	18

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 z (sin.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 z (sin.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 z (sin.f64 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 z (sin.f64 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 z 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (sin.f64 y))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x (cos.f64 y)) 1) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) 2) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x .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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 z (sin.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (sin.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 z 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (sin.f64 y))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z (sin.f64 y)) (*.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (cos.f64 y)) 1) (*.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3) (pow.f64 (*.f64 z (sin.f64 y)) 3)) (+.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (-.f64 (pow.f64 (*.f64 z (sin.f64 y)) 2) (*.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (cos.f64 y)) (*.f64 x (cos.f64 y))) (pow.f64 (*.f64 z (sin.f64 y)) 2)) (-.f64 (*.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))))

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

609×	`distribute-rgt-neg-in_binary64`
502×	`associate-l_binary64`
420×	`fma-neg_binary64`
410×	`associate-r_binary64`
226×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	600
1	117	592
2	353	580
3	1244	579
4	3964	579

Stop Event

1×	node limit

Counts

96 → 54

Calls

Call 1

Inputs
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 y z)
(-.f64 (.f64 y z) (.f64 1/6 (*.f64 (pow.f64 y 3) z)))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) z)) (.f64 y z)) (.f64 1/6 (*.f64 (pow.f64 y 3) z)))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) z)) (.f64 y z)) (+.f64 (.f64 1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
x
(+.f64 (*.f64 y z) x)
(-.f64 (+.f64 (.f64 y z) x) (.f64 1/2 (*.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))

Outputs
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 y z)
(-.f64 (.f64 y z) (.f64 1/6 (*.f64 (pow.f64 y 3) z)))
(-.f64 (.f64 y z) (.f64 1/6 (*.f64 z (pow.f64 y 3))))
(.f64 z (-.f64 y (.f64 1/6 (pow.f64 y 3))))
(.f64 z (+.f64 y (.f64 (pow.f64 y 3) -1/6)))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) z)) (.f64 y z)) (.f64 1/6 (*.f64 (pow.f64 y 3) z)))
(+.f64 (fma.f64 1/120 (.f64 z (pow.f64 y 5)) (.f64 y z)) (.f64 -1/6 (.f64 z (pow.f64 y 3))))
(fma.f64 1/120 (.f64 z (pow.f64 y 5)) (.f64 z (-.f64 y (*.f64 1/6 (pow.f64 y 3)))))
(.f64 z (-.f64 (fma.f64 1/120 (pow.f64 y 5) y) (.f64 1/6 (pow.f64 y 3))))
(.f64 z (+.f64 (fma.f64 1/120 (pow.f64 y 5) (.f64 (pow.f64 y 3) -1/6)) y))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) z)) (.f64 y z)) (+.f64 (.f64 1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(-.f64 (fma.f64 1/120 (.f64 z (pow.f64 y 5)) (.f64 y z)) (fma.f64 1/5040 (.f64 z (pow.f64 y 7)) (.f64 1/6 (*.f64 z (pow.f64 y 3)))))
(-.f64 (.f64 z (+.f64 y (.f64 1/120 (pow.f64 y 5)))) (.f64 z (+.f64 (.f64 1/6 (pow.f64 y 3)) (*.f64 1/5040 (pow.f64 y 7)))))
(.f64 z (-.f64 (fma.f64 1/120 (pow.f64 y 5) y) (fma.f64 1/5040 (pow.f64 y 7) (.f64 1/6 (pow.f64 y 3)))))
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
x
(+.f64 (*.f64 y z) x)
(fma.f64 y z x)
(-.f64 (+.f64 (.f64 y z) x) (.f64 1/2 (*.f64 (pow.f64 y 2) x)))
(+.f64 (fma.f64 y z x) (.f64 -1/2 (.f64 x (*.f64 y y))))
(+.f64 (fma.f64 y z x) (.f64 (.f64 x (*.f64 y y)) -1/2))
(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
(-.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(-.f64 (fma.f64 y z x) (fma.f64 1/2 (.f64 x (.f64 y y)) (.f64 1/6 (.f64 z (pow.f64 y 3)))))
(-.f64 (fma.f64 y z x) (fma.f64 1/6 (.f64 z (pow.f64 y 3)) (.f64 x (.f64 1/2 (.f64 y y)))))
(+.f64 (fma.f64 y z x) (fma.f64 (.f64 z (pow.f64 y 3)) -1/6 (.f64 x (.f64 (.f64 y y) -1/2))))
(-.f64 (fma.f64 y z x) (.f64 (.f64 y y) (-.f64 (.f64 y (.f64 z 1/6)) (*.f64 x -1/2))))
(+.f64 x (fma.f64 z (+.f64 y (.f64 (pow.f64 y 3) -1/6)) (.f64 (.f64 x (.f64 y y)) -1/2)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 (sin.f64 y) z))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))

prune39.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	47	7	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	7	55

Error

0.1b

Counts

55 → 7

Alt Table

Status	Error	Program
	39.8b	(cbrt.f64 (pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 3))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	0.1b	(pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 1)
	40.2b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	1.4b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))
	26.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))

Compiler

Compiled 967 to 400 computations (58.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.1%)

Counts

2 → 40

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(*.f64 (cos.f64 y) x)
1.0ms	x	@	0	(*.f64 (cos.f64 y) x)
1.0ms	z	@	-inf	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
0.0ms	x	@	inf	(*.f64 (cos.f64 y) x)
0.0ms	y	@	inf	(*.f64 (cos.f64 y) x)

rewrite44.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`pow1_binary64`
689×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
81×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1853	18

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 y) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 y) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (cos.f64 y) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (cos.f64 y) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 y) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sin.f64 y) z) (.f64 (cos.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (sin.f64 y) z) 1) (.f64 (cos.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) (pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) 2) (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) (sqrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (sin.f64 y) z) 3) (pow.f64 (.f64 (cos.f64 y) x) 3)) (+.f64 (.f64 (.f64 (sin.f64 y) z) (.f64 (sin.f64 y) z)) (-.f64 (pow.f64 (.f64 (cos.f64 y) x) 2) (.f64 (.f64 (sin.f64 y) z) (.f64 (cos.f64 y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 (sin.f64 y) z) (.f64 (sin.f64 y) z)) (pow.f64 (.f64 (cos.f64 y) x) 2)) (-.f64 (.f64 (sin.f64 y) z) (.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 y) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 y) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 y) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 y) x)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 y) x) (*.f64 (sin.f64 y) z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sin.f64 y) z) (*.f64 (cos.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sin.f64 y) z) 1) (*.f64 (cos.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) (pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 2) (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) (sqrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3) (pow.f64 (*.f64 (cos.f64 y) x) 3)) (+.f64 (*.f64 (*.f64 (sin.f64 y) z) (*.f64 (sin.f64 y) z)) (-.f64 (pow.f64 (*.f64 (cos.f64 y) x) 2) (*.f64 (*.f64 (sin.f64 y) z) (*.f64 (cos.f64 y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (sin.f64 y) z) (*.f64 (sin.f64 y) z)) (pow.f64 (*.f64 (cos.f64 y) x) 2)) (-.f64 (*.f64 (sin.f64 y) z) (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))))

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

739×	`cancel-sign-sub-inv_binary64`
698×	`fma-def_binary64`
361×	`fma-neg_binary64`
271×	`sub-neg_binary64`
240×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	468
1	107	467
2	324	457
3	1258	450
4	4705	450

Stop Event

1×	node limit

Counts

76 → 54

Calls

Call 1

Inputs
x
(-.f64 x (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (+.f64 (.f64 1/720 (.f64 (pow.f64 y 6) x)) (.f64 1/2 (.f64 (pow.f64 y 2) x))))
x
(+.f64 (*.f64 y z) x)
(-.f64 (+.f64 (.f64 y z) x) (.f64 1/2 (*.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))

Outputs
x
(-.f64 x (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 x (.f64 -1/2 (.f64 x (*.f64 y y))))
(+.f64 x (.f64 (.f64 -1/2 x) (*.f64 y y)))
(fma.f64 (.f64 (.f64 y y) -1/2) x x)
(.f64 x (fma.f64 (.f64 y y) -1/2 1))
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (.f64 -1/2 (.f64 x (.f64 y y))))
(+.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (.f64 (.f64 -1/2 x) (.f64 y y)))
(.f64 x (-.f64 (fma.f64 1/24 (pow.f64 y 4) 1) (.f64 1/2 (*.f64 y y))))
(fma.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 y (.f64 y -1/2))) x)
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (+.f64 (.f64 1/720 (.f64 (pow.f64 y 6) x)) (.f64 1/2 (.f64 (pow.f64 y 2) x))))
(-.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (fma.f64 1/720 (.f64 x (pow.f64 y 6)) (.f64 1/2 (.f64 x (*.f64 y y)))))
(-.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (.f64 x (+.f64 (.f64 1/2 (.f64 y y)) (*.f64 1/720 (pow.f64 y 6)))))
(+.f64 x (.f64 x (-.f64 (.f64 1/24 (pow.f64 y 4)) (fma.f64 1/2 (.f64 y y) (.f64 1/720 (pow.f64 y 6))))))
(fma.f64 x (-.f64 (.f64 1/24 (pow.f64 y 4)) (fma.f64 1/720 (pow.f64 y 6) (.f64 1/2 (*.f64 y y)))) x)
x
(+.f64 (*.f64 y z) x)
(fma.f64 y z x)
(-.f64 (+.f64 (.f64 y z) x) (.f64 1/2 (*.f64 (pow.f64 y 2) x)))
(-.f64 (fma.f64 y z x) (.f64 1/2 (.f64 x (*.f64 y y))))
(-.f64 (fma.f64 y z x) (.f64 x (.f64 1/2 (*.f64 y y))))
(fma.f64 y z (fma.f64 (.f64 (.f64 y y) -1/2) x x))
(fma.f64 x (.f64 y (.f64 y -1/2)) (fma.f64 y z x))
(-.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(-.f64 (fma.f64 y z x) (fma.f64 1/2 (.f64 x (.f64 y y)) (.f64 1/6 (.f64 z (pow.f64 y 3)))))
(-.f64 (fma.f64 y z x) (fma.f64 1/2 (.f64 x (.f64 y y)) (.f64 z (.f64 1/6 (pow.f64 y 3)))))
(+.f64 (fma.f64 y z (fma.f64 (.f64 (.f64 y y) -1/2) x x)) (.f64 z (.f64 (pow.f64 y 3) -1/6)))
(fma.f64 (fma.f64 (.f64 y y) -1/2 1) x (.f64 z (-.f64 y (*.f64 1/6 (pow.f64 y 3)))))
(fma.f64 (fma.f64 (.f64 y y) -1/2 1) x (.f64 z (+.f64 y (*.f64 (pow.f64 y 3) -1/6))))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y)))

prune39.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	56	5	61

Error

0.1b

Counts

61 → 5

Alt Table

Status	Error	Program
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
▶	0.1b	(pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 1)
	28.1b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))
	1.0b	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))
	26.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))

Compiler

Compiled 826 to 344 computations (58.4% saved)

localize9.0ms (0.2%)

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))

prune36.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	54	5	59

Error

0.1b

Counts

59 → 5

Alt Table

Status	Error	Program
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
✓	0.1b	(pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 1)
	28.1b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))
▶	1.0b	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))
	26.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))

Compiler

Compiled 938 to 449 computations (52.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))
	0.2b	(*.f64 (cos.f64 y) x)
✓	0.6b	(cbrt.f64 (*.f64 (cos.f64 y) x))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)

series24.0ms (0.6%)

Counts

3 → 51

Calls

21 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)
4.0ms	y	@	0	(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)
2.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)
2.0ms	y	@	inf	(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)
2.0ms	y	@	inf	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))

rewrite48.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

863×	`log1p-expm1-u_binary64`
863×	`expm1-log1p-u_binary64`
102×	`add-sqr-sqrt_binary64`
98×	`pow1_binary64`
97×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	227	26
2	2378	26

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3)
(cbrt.f64 (*.f64 (cos.f64 y) x))
(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 y) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (cos.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 y) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (cos.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) (cbrt.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.f64 (cos.f64 y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (cos.f64 y) x)) (sqrt.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cos.f64 y) x) 1/6) (*.f64 (pow.f64 (*.f64 (cos.f64 y) x) 1/6) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 y)) (*.f64 (sqrt.f64 (cos.f64 y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) 2) 3) (cbrt.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (cos.f64 y) x) 1/6) 3) (pow.f64 (pow.f64 (*.f64 (cos.f64 y) x) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) 1) (cbrt.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) (cbrt.f64 (cos.f64 y))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) (pow.f64 (*.f64 (cos.f64 y) x) 1/6)) (pow.f64 (*.f64 (cos.f64 y) x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 y) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 y) x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) 2) (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cos.f64 y) x) 1/6) (pow.f64 (*.f64 (cos.f64 y) x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (cos.f64 y) x)) 1/3) (pow.f64 (sqrt.f64 (*.f64 (cos.f64 y) x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 y) x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 y) x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 y) x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 (cos.f64 y) x))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 y) x) (*.f64 (sin.f64 y) z))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sin.f64 y) z) (*.f64 (cos.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sin.f64 y) z) 1) (*.f64 (cos.f64 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) (pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 2) (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) (sqrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3) (pow.f64 (*.f64 (cos.f64 y) x) 3)) (+.f64 (*.f64 (*.f64 (sin.f64 y) z) (*.f64 (sin.f64 y) z)) (-.f64 (pow.f64 (*.f64 (cos.f64 y) x) 2) (*.f64 (*.f64 (sin.f64 y) z) (*.f64 (cos.f64 y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (sin.f64 y) z) (*.f64 (sin.f64 y) z)) (pow.f64 (*.f64 (cos.f64 y) x) 2)) (-.f64 (*.f64 (sin.f64 y) z) (*.f64 (cos.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))))))))

simplify33.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
471×	`distribute-rgt-neg-in_binary64`
468×	`distribute-lft-neg-in_binary64`
278×	`associate-r_binary64`
260×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	562
1	163	555
2	532	536
3	2452	531

Stop Event

1×	node limit

Counts

133 → 107

Calls

Call 1

Inputs
x
(-.f64 x (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (+.f64 (.f64 1/720 (.f64 (pow.f64 y 6) x)) (.f64 1/2 (.f64 (pow.f64 y 2) x))))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(pow.f64 x 1/3)
(-.f64 (pow.f64 x 1/3) (.f64 1/6 (.f64 (pow.f64 y 2) (pow.f64 x 1/3))))
(-.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/72 (.f64 (pow.f64 y 4) (pow.f64 x 1/3))) (.f64 1/6 (.f64 (pow.f64 y 2) (pow.f64 x 1/3)))))
(-.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/72 (.f64 (pow.f64 y 4) (pow.f64 x 1/3))) (+.f64 (.f64 1/6 (.f64 (pow.f64 y 2) (pow.f64 x 1/3))) (.f64 23/6480 (.f64 (pow.f64 y 6) (pow.f64 x 1/3))))))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
x
(+.f64 (*.f64 y z) x)
(-.f64 (+.f64 (.f64 y z) x) (.f64 1/2 (*.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)
(*.f64 (sin.f64 y) z)

Outputs
x
(-.f64 x (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 x (.f64 -1/2 (.f64 x (*.f64 y y))))
(+.f64 x (.f64 (.f64 -1/2 x) (*.f64 y y)))
(fma.f64 (.f64 x -1/2) (.f64 y y) x)
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (.f64 1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (.f64 -1/2 (.f64 x (.f64 y y))))
(+.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (.f64 (.f64 -1/2 x) (.f64 y y)))
(.f64 x (-.f64 (fma.f64 1/24 (pow.f64 y 4) 1) (.f64 1/2 (*.f64 y y))))
(+.f64 x (.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 y (*.f64 y -1/2)))))
(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) x) (+.f64 (.f64 1/720 (.f64 (pow.f64 y 6) x)) (.f64 1/2 (.f64 (pow.f64 y 2) x))))
(-.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (fma.f64 1/720 (.f64 x (pow.f64 y 6)) (.f64 1/2 (.f64 x (*.f64 y y)))))
(-.f64 (fma.f64 1/24 (.f64 x (pow.f64 y 4)) x) (.f64 x (+.f64 (.f64 1/2 (.f64 y y)) (*.f64 1/720 (pow.f64 y 6)))))
(+.f64 x (.f64 x (-.f64 (.f64 1/24 (pow.f64 y 4)) (fma.f64 1/2 (.f64 y y) (.f64 1/720 (pow.f64 y 6))))))
(.f64 x (-.f64 (fma.f64 1/24 (pow.f64 y 4) 1) (fma.f64 1/2 (.f64 y y) (*.f64 1/720 (pow.f64 y 6)))))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(pow.f64 x 1/3)
(cbrt.f64 x)
(-.f64 (pow.f64 x 1/3) (.f64 1/6 (.f64 (pow.f64 y 2) (pow.f64 x 1/3))))
(+.f64 (cbrt.f64 x) (.f64 -1/6 (.f64 (*.f64 y y) (cbrt.f64 x))))
(+.f64 (cbrt.f64 x) (.f64 (.f64 y (*.f64 y (cbrt.f64 x))) -1/6))
(fma.f64 (.f64 y (.f64 y (cbrt.f64 x))) -1/6 (cbrt.f64 x))
(-.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/72 (.f64 (pow.f64 y 4) (pow.f64 x 1/3))) (.f64 1/6 (.f64 (pow.f64 y 2) (pow.f64 x 1/3)))))
(-.f64 (cbrt.f64 x) (fma.f64 1/72 (.f64 (pow.f64 y 4) (cbrt.f64 x)) (.f64 1/6 (.f64 (.f64 y y) (cbrt.f64 x)))))
(-.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (+.f64 (.f64 (.f64 y y) 1/6) (.f64 (pow.f64 y 4) 1/72))))
(-.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (fma.f64 (.f64 y y) 1/6 (*.f64 (pow.f64 y 4) 1/72))))
(-.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/72 (.f64 (pow.f64 y 4) (pow.f64 x 1/3))) (+.f64 (.f64 1/6 (.f64 (pow.f64 y 2) (pow.f64 x 1/3))) (.f64 23/6480 (.f64 (pow.f64 y 6) (pow.f64 x 1/3))))))
(-.f64 (cbrt.f64 x) (fma.f64 1/72 (.f64 (pow.f64 y 4) (cbrt.f64 x)) (fma.f64 1/6 (.f64 (.f64 y y) (cbrt.f64 x)) (.f64 23/6480 (*.f64 (pow.f64 y 6) (cbrt.f64 x))))))
(-.f64 (cbrt.f64 x) (fma.f64 1/72 (.f64 (pow.f64 y 4) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (+.f64 (.f64 (.f64 y y) 1/6) (*.f64 (pow.f64 y 6) 23/6480)))))
(-.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (+.f64 (.f64 (pow.f64 y 4) 1/72) (fma.f64 (.f64 y y) 1/6 (.f64 (pow.f64 y 6) 23/6480)))))
(.f64 (cbrt.f64 x) (-.f64 (+.f64 (.f64 (pow.f64 y 4) -1/72) 1) (fma.f64 (pow.f64 y 6) 23/6480 (.f64 y (.f64 y 1/6)))))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) x) 1/3)
(cbrt.f64 (*.f64 x (cos.f64 y)))
x
(+.f64 (*.f64 y z) x)
(fma.f64 y z x)
(-.f64 (+.f64 (.f64 y z) x) (.f64 1/2 (*.f64 (pow.f64 y 2) x)))
(+.f64 (fma.f64 y z x) (.f64 -1/2 (.f64 x (*.f64 y y))))
(-.f64 (fma.f64 y z x) (.f64 (.f64 y y) (*.f64 x 1/2)))
(fma.f64 (.f64 x -1/2) (.f64 y y) (fma.f64 y z x))
(-.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 1/2 (.f64 (pow.f64 y 2) x)) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
(-.f64 (fma.f64 y z x) (fma.f64 1/2 (.f64 x (.f64 y y)) (.f64 1/6 (.f64 z (pow.f64 y 3)))))
(-.f64 (fma.f64 y z x) (fma.f64 1/2 (.f64 x (.f64 y y)) (.f64 (pow.f64 y 3) (.f64 z 1/6))))
(+.f64 x (fma.f64 y z (fma.f64 (.f64 x -1/2) (.f64 y y) (.f64 (.f64 -1/6 z) (pow.f64 y 3)))))
(+.f64 (fma.f64 (.f64 x -1/2) (.f64 y y) x) (.f64 z (-.f64 y (.f64 1/6 (pow.f64 y 3)))))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 (sin.f64 y) z))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))
(*.f64 (sin.f64 y) z)
(*.f64 z (sin.f64 y))

prune83.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	125	8	133

Error

0.0b

Counts

133 → 8

Alt Table

Status	Error	Program
	26.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
	16.3b	(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 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x)))
	34.2b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
✓	0.1b	(pow.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))) 1)
✓	1.0b	(fma.f64 (sin.f64 y) z (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 3))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 y) x)) 2) (cbrt.f64 (cos.f64 y))) (cbrt.f64 x)))

Compiler

Compiled 2064 to 863 computations (58.2% saved)

regimes155.0ms (3.6%)

Accuracy

Total 0.1b remaining (45.5%)

Threshold costs 0.1b (45.5%)

Counts

61 → 1

Compiler

Compiled 658 to 204 computations (69% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	15	12

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (sin.f64 y) z (.f64 1 (.f64 (cos.f64 y) x)))

Outputs
(fma.f64 (sin.f64 y) z (.f64 1 (.f64 (cos.f64 y) x)))
(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))

end116.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 151 to 100 computations (33.8% saved)

Details

analyze493.0ms (11.3%)

sample3.0s (70%)

preprocess19.0ms (0.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series10.0ms (0.2%)

rewrite40.0ms (0.9%)

simplify41.0ms (0.9%)

prune39.0ms (0.9%)

localize7.0ms (0.2%)

series6.0ms (0.1%)

rewrite44.0ms (1%)

simplify37.0ms (0.8%)

prune39.0ms (0.9%)

localize9.0ms (0.2%)

prune36.0ms (0.8%)

localize10.0ms (0.2%)

series24.0ms (0.6%)

rewrite48.0ms (1.1%)

simplify33.0ms (0.8%)

prune83.0ms (1.9%)

regimes155.0ms (3.6%)

simplify2.0ms (0%)

end116.0ms (2.7%)

Profiling