Details

analyze441.0ms (4.4%)

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
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.8s (28.1%)

Results

1.3s	2080×	body	1024	valid
993.0ms	5131×	body	256	valid
498.0ms	1036×	body	512	valid
8.0ms	9×	body	2048	valid

preprocess21.0ms (0.2%)

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 15 to 11 computations (26.7% saved)

simplify8.0ms (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)))

eval1.0ms (0%)

Compiler: Compiled 20 to 9 computations (55% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 27 to 8 computations (70.4% saved)

series26.0ms (0.3%)

Counts

4 → 68

Calls

24 calls:

Time	Variable		Point	Expression
7.0ms	z	@	-inf	(*.f64 z (sin.f64 y))
1.0ms	y	@	inf	(cos.f64 y)
1.0ms	y	@	0	(*.f64 z (sin.f64 y))
1.0ms	x	@	0	(*.f64 x (cos.f64 y))
1.0ms	z	@	0	(*.f64 z (sin.f64 y))

rewrite122.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

484×	`log-prod_binary64`
382×	`prod-exp_binary64`
361×	`exp-prod_binary64`
332×	`pow-prod-down_binary64`
325×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	187	27
2	2497	27

Stop Event

1×	node limit

Counts

4 → 167

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (cos.f64 y))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (cos.f64 y)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (cos.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (cos.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (cos.f64 y)))) 2)) (cbrt.f64 (log.f64 (.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (cos.f64 y))))) (sqrt.f64 (log.f64 (.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (cos.f64 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (cos.f64 y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (cos.f64 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 x (cos.f64 y)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 x (cos.f64 y))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 x (cos.f64 y))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 x) 1) (log.f64 (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 x) (.f64 (log.f64 (cos.f64 y)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (cos.f64 y)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 (cos.f64 y)) 1) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (cos.f64 y)) (.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 (cos.f64 y)) 1) (*.f64 (log.f64 x) 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (sin.f64 y))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (sin.f64 y)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (sin.f64 y)))))))) (#(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)) 2) 1/2)))) (#(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 pow.f64 (pow.f64 (.f64 z (sin.f64 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 z (sin.f64 y)))) 2)) (cbrt.f64 (log.f64 (.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 z (sin.f64 y))))) (sqrt.f64 (log.f64 (.f64 z (sin.f64 y)))))))) (#(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 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 exp.f64 (log.f64 (.f64 z (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 z (sin.f64 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 z (sin.f64 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 z (sin.f64 y))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 z (sin.f64 y))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 z) 1) (log.f64 (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 z) (.f64 (log.f64 (sin.f64 y)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 z) 1) (.f64 (log.f64 (sin.f64 y)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 (sin.f64 y)) 1) (log.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sin.f64 y)) (.f64 (log.f64 z) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 (log.f64 (sin.f64 y)) 1) (.f64 (log.f64 z) 1)))))))
((#(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 (/.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (fma.f64 x (cos.f64 y) (.f64 (neg.f64 z) (sin.f64 y)))) (/.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (fma.f64 x (cos.f64 y) (.f64 (neg.f64 z) (sin.f64 y)))))))) (#(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 1 (fma.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 x (cos.f64 y)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2)) (/.f64 1 (fma.f64 x (cos.f64 y) (.f64 (neg.f64 z) (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 x (cos.f64 y)) 2)) (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x (cos.f64 y) (.f64 (neg.f64 z) (sin.f64 y))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2))))))) (#(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)) (fma.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 x (cos.f64 y)) 2)))))) (#(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 (pow.f64 (.f64 z (sin.f64 y)) 2) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (.f64 (.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)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2)) (fma.f64 x (cos.f64 y) (.f64 (neg.f64 z) (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3))) (neg.f64 (fma.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 x (cos.f64 y)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2))) (neg.f64 (fma.f64 x (cos.f64 y) (.f64 (neg.f64 z) (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (pow.f64 (.f64 x (cos.f64 y)) 2)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.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))) 2) 1/2)))) (#(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 pow.f64 (exp.f64 1) (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (.f64 z (sin.f64 y)) (-.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 x (cos.f64 y)) 2)) (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x (cos.f64 y) (.f64 (neg.f64 z) (sin.f64 y))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) 2)) (cbrt.f64 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))) (sqrt.f64 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))))))) (#(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 log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x (cos.f64 y)))) (pow.f64 (exp.f64 z) (sin.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 x) (cos.f64 y)) (+.f64 1 (expm1.f64 (.f64 z (sin.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x (cos.f64 y)))) (+.f64 1 (expm1.f64 (.f64 z (sin.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 z (sin.f64 y)))) (pow.f64 (exp.f64 x) (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 z) (sin.f64 y)) (+.f64 1 (expm1.f64 (.f64 x (cos.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 z (sin.f64 y)))) (+.f64 1 (expm1.f64 (.f64 x (cos.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 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)))))))) (#(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 exp.f64 (.f64 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 y) x (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (cos.f64 y)) 1 (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 z (sin.f64 y) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sin.f64 y) z (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 z (sin.f64 y)) 1 (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (cbrt.f64 (.f64 z (sin.f64 y))) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2) (cbrt.f64 (.f64 x (cos.f64 y))) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y)) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) (sin.f64 y)) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) z) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y))) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y))) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y)) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) z) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) (.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 z (sin.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 z (sin.f64 y)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 y))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 y))) (sin.f64 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 y))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (cos.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (pow.f64 (cos.f64 y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (cbrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cos.f64 y)) (sqrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 y) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cos.f64 y))) 2)) (cbrt.f64 (log.f64 (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (cos.f64 y)))) (sqrt.f64 (log.f64 (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cos.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (cos.f64 y) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (cos.f64 y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (cos.f64 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 (log.f64 (cos.f64 y)) 1) 1))))))

simplify223.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

682×	`sqr-pow_binary64`
626×	`cube-prod_binary64`
460×	`*-commutative_binary64`
443×	`pow-sqr_binary64`
408×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	706
1	165	699
2	449	676
3	1471	674
4	2337	674
5	3446	674
6	3584	674
7	3801	674
8	4016	674
9	4298	674
10	4713	674
11	5214	674
12	5790	674
13	6480	674
14	6990	674
15	7384	674
16	7770	674

Stop Event

1×	node limit

Counts

235 → 198

Calls

Call 1

Inputs
(*.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)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) 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)
(*.f64 y z)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
x
(+.f64 (*.f64 y z) x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (.f64 1/24 (pow.f64 y 4))))
(+.f64 (.f64 -1/720 (pow.f64 y 6)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (*.f64 1/24 (pow.f64 y 4)))))

Outputs
(*.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)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(.f64 (fma.f64 -1/2 (.f64 y y) 1) x)
(.f64 x (fma.f64 y (.f64 y -1/2) 1))
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(+.f64 x (.f64 x (fma.f64 -1/2 (.f64 y y) (*.f64 1/24 (pow.f64 y 4)))))
(.f64 x (fma.f64 y (.f64 y -1/2) (fma.f64 1/24 (pow.f64 y 4) 1)))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (+.f64 x (.f64 x (fma.f64 -1/2 (.f64 y y) (.f64 1/24 (pow.f64 y 4))))))
(+.f64 x (.f64 x (fma.f64 -1/720 (pow.f64 y 6) (fma.f64 y (.f64 y -1/2) (*.f64 1/24 (pow.f64 y 4))))))
(.f64 x (fma.f64 -1/720 (pow.f64 y 6) (fma.f64 y (.f64 y -1/2) (fma.f64 1/24 (pow.f64 y 4) 1))))
(*.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)
(*.f64 y z)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 y z))
(.f64 z (+.f64 y (.f64 -1/6 (pow.f64 y 3))))
(*.f64 z (fma.f64 -1/6 (pow.f64 y 3) y))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (.f64 1/120 (*.f64 z (pow.f64 y 5)))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 z (+.f64 (*.f64 1/120 (pow.f64 y 5)) y)))
(.f64 z (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (.f64 1/120 (pow.f64 y 5))))
(.f64 z (+.f64 (.f64 -1/6 (pow.f64 y 3)) (fma.f64 1/120 (pow.f64 y 5) y)))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (fma.f64 -1/5040 (.f64 z (pow.f64 y 7)) (.f64 1/120 (.f64 z (pow.f64 y 5))))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (.f64 z (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))))
(.f64 z (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7)))))
(.f64 z (+.f64 (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))) (fma.f64 -1/6 (pow.f64 y 3) y)))
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
x
(+.f64 (*.f64 y z) x)
(fma.f64 y z x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x))
(fma.f64 y z (fma.f64 -1/2 (.f64 x (.f64 y y)) x))
(fma.f64 y z (.f64 (fma.f64 -1/2 (.f64 y y) 1) x))
(fma.f64 x (.f64 y (.f64 y -1/2)) (fma.f64 y z x))
(fma.f64 y z (.f64 x (fma.f64 y (.f64 y -1/2) 1)))
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x)))
(fma.f64 y z (fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x)))
(fma.f64 y z (fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 (fma.f64 -1/2 (*.f64 y y) 1) x)))
(fma.f64 z (fma.f64 -1/6 (pow.f64 y 3) y) (.f64 x (fma.f64 y (.f64 y -1/2) 1)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(*.f64 (cos.f64 y) x)
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 (cos.f64 y) x))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) (*.f64 (cos.f64 y) x))
(fma.f64 (cos.f64 y) x (*.f64 z (sin.f64 y)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 y 2)))
(+.f64 1 (.f64 -1/2 (.f64 y y)))
(fma.f64 -1/2 (*.f64 y y) 1)
(fma.f64 y (*.f64 y -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (.f64 1/24 (pow.f64 y 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 y y) (.f64 1/24 (pow.f64 y 4))))
(+.f64 (fma.f64 -1/2 (.f64 y y) 1) (.f64 1/24 (pow.f64 y 4)))
(fma.f64 y (*.f64 y -1/2) (fma.f64 1/24 (pow.f64 y 4) 1))
(+.f64 (.f64 -1/720 (pow.f64 y 6)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (*.f64 1/24 (pow.f64 y 4)))))
(fma.f64 -1/720 (pow.f64 y 6) (+.f64 1 (fma.f64 -1/2 (.f64 y y) (.f64 1/24 (pow.f64 y 4)))))
(fma.f64 -1/720 (pow.f64 y 6) (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (.f64 1/24 (pow.f64 y 4))))
(fma.f64 -1/720 (pow.f64 y 6) (fma.f64 y (*.f64 y -1/2) (fma.f64 1/24 (pow.f64 y 4) 1)))

eval42.0ms (0.4%)

Compiler: Compiled 2987 to 1031 computations (65.5% saved)

prune57.0ms (0.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	178	20	198
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	21	199

Error

0.0b

Counts

199 → 21

Alt Table

Click to see full alt table

Status	Error	Program
▶	24.0b	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
	2.9b	(fma.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) z) (.f64 x (cos.f64 y)))
	15.1b	(+.f64 (.f64 x (pow.f64 (sqrt.f64 (cos.f64 y)) 2)) (.f64 z (sin.f64 y)))
	33.5b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))
	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
	32.5b	(+.f64 (.f64 y z) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x))
	29.6b	(fma.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) (.f64 x (cos.f64 y)))
	31.2b	(fma.f64 y z x)
	0.6b	(fma.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (.f64 x (cos.f64 y)))
▶	31.2b	(+.f64 (*.f64 y z) x)
	0.2b	(+.f64 (.f64 x (log1p.f64 (expm1.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
▶	29.9b	(+.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))
	39.7b	(*.f64 z (sin.f64 y))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))
	18.9b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
	0.3b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 z (sin.f64 y)))
▶	0.9b	(+.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
	15.7b	(+.f64 x (*.f64 z (sin.f64 y)))
	0.3b	(+.f64 (.f64 x (-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1)) (.f64 z (sin.f64 y)))
	0.2b	(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))

Compiler

Compiled 554 to 382 computations (31% saved)

localize13.0ms (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 x (cos.f64 y)))
	0.1b	(*.f64 x (cos.f64 y))

Compiler

Compiled 22 to 7 computations (68.2% saved)

series4.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`pow1_binary64`
689×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
672×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	156	12
2	1853	12

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

Outputs

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

simplify173.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary64`
757×	`sqr-pow_binary64`
556×	`distribute-lft-out_binary64`
466×	`*-commutative_binary64`
374×	`pow-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	394
1	67	394
2	160	393
3	420	391
4	1355	388
5	2736	388
6	4205	388
7	4323	388
8	4496	388
9	4704	388
10	5040	388
11	5396	388
12	5872	388
13	6412	388
14	7076	388
15	7908	388

Stop Event

1×	node limit

Counts

57 → 34

Calls

Call 1

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

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y z) x)

Compiler

Compiled 14 to 5 computations (64.3% saved)

series5.0ms (0.1%)

Counts

1 → 9

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	z	@	-inf	(+.f64 (*.f64 y z) x)
0.0ms	x	@	inf	(+.f64 (*.f64 y z) x)
0.0ms	y	@	0	(+.f64 (*.f64 y z) x)
0.0ms	z	@	inf	(+.f64 (*.f64 y z) x)
0.0ms	y	@	inf	(+.f64 (*.f64 y z) x)

rewrite58.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`pow1_binary64`
655×	`add-log-exp_binary64`
655×	`log1p-expm1-u_binary64`
655×	`expm1-log1p-u_binary64`
640×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	5
1	129	5
2	1775	5

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(+.f64 (*.f64 y z) x)

Outputs

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	24
1	6	24

Stop Event

1×

saturated

Counts

44 → 37

Calls

Call 1

Inputs
x
(*.f64 y z)
(*.f64 y z)
x
(*.f64 y z)
(*.f64 y z)
(*.f64 y z)
x
x

Outputs
x
(*.f64 y z)
(*.f64 y z)
x
(*.f64 y z)
(*.f64 y z)
(*.f64 y z)
x
x

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 23 to 7 computations (69.6% saved)

series3.0ms (0%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
0.0ms	y	@	0	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
0.0ms	x	@	inf	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
0.0ms	z	@	-inf	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
0.0ms	y	@	-inf	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))

rewrite60.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

911×	`pow1_binary64`
841×	`add-log-exp_binary64`
841×	`log1p-expm1-u_binary64`
841×	`expm1-log1p-u_binary64`
822×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	168	10
2	2280	10

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

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

Outputs

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

simplify185.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
671×	`sqr-pow_binary64`
476×	`distribute-lft-out_binary64`
444×	`cube-prod_binary64`
426×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	324
1	58	324
2	139	321
3	375	321
4	1285	318
5	2767	318
6	3925	318
7	4006	318
8	4129	318
9	4284	318
10	4546	318
11	4805	318
12	5158	318
13	5535	318
14	6026	318
15	6613	318
16	7331	318
17	7661	318
18	7923	318

Stop Event

1×	node limit

Counts

73 → 48

Calls

Call 1

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

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

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
	0.1b	(*.f64 x (cos.f64 y))
✓	0.2b	(pow.f64 (*.f64 x (cos.f64 y)) 3)
✓	39.8b	(cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3))

Compiler

Compiled 44 to 17 computations (61.4% saved)

series11.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(pow.f64 (*.f64 x (cos.f64 y)) 3)
2.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3))
1.0ms	y	@	0	(pow.f64 (*.f64 x (cos.f64 y)) 3)
1.0ms	y	@	-inf	(pow.f64 (*.f64 x (cos.f64 y)) 3)
1.0ms	x	@	-inf	(pow.f64 (*.f64 x (cos.f64 y)) 3)

rewrite59.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

645×	`pow1_binary64`
603×	`add-log-exp_binary64`
603×	`log1p-expm1-u_binary64`
603×	`expm1-log1p-u_binary64`
586×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	168	15
2	1728	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

649×	`distribute-rgt-out_binary64`
558×	`distribute-rgt-in_binary64`
552×	`fma-def_binary64`
549×	`distribute-lft-in_binary64`
452×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	596
1	208	584
2	787	556
3	4122	546
4	7923	546

Stop Event

1×	node limit

Counts

102 → 70

Calls

Call 1

Inputs
(*.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)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) 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)
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(pow.f64 x 3)
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3)))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 6) (+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2))) x)) (+.f64 (.f64 (+.f64 (.f64 -1/360 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 2))) x) (.f64 -1/720 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))

Outputs
(*.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)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(fma.f64 (.f64 (.f64 -1/2 y) y) x x)
(.f64 x (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 x (.f64 y (.f64 y -1/2)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 (.f64 (*.f64 -1/2 y) y) x x))
(fma.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 y (.f64 y -1/2))) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 (.f64 (.f64 -1/2 y) y) x x)))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 1/24 (pow.f64 y 4))) (.f64 x (fma.f64 -1/2 (*.f64 y y) 1)))
(.f64 x (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(*.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)
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(pow.f64 x 3)
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))
(fma.f64 (.f64 y y) (.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))
(fma.f64 y (.f64 y (.f64 (pow.f64 x 3) -3/2)) (pow.f64 x 3))
(.f64 (+.f64 (.f64 (*.f64 -3/2 y) y) 1) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3)))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) 1/3) (.f64 (pow.f64 x 3) 13/24)) (pow.f64 y 4) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 4) (fma.f64 (pow.f64 x 3) 13/24 (.f64 (pow.f64 x 3) 1/3)) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3)))
(fma.f64 y (.f64 y (.f64 (pow.f64 x 3) -3/2)) (fma.f64 (pow.f64 y 4) (*.f64 (pow.f64 x 3) 7/8) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (.f64 (+.f64 (.f64 (.f64 -3/2 y) y) 1) (pow.f64 x 3)))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 6) (+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2))) x)) (+.f64 (.f64 (+.f64 (.f64 -1/360 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 2))) x) (.f64 -1/720 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) 1/3) (.f64 (pow.f64 x 3) 13/24)) (pow.f64 y 4) (fma.f64 (pow.f64 y 6) (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 -1/2 (.f64 x (.f64 (.f64 x x) 1/3)) (fma.f64 (.f64 (.f64 x x) -2/45) x (.f64 -1/720 (pow.f64 x 3))))) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (fma.f64 (pow.f64 x 3) 13/24 (.f64 (pow.f64 x 3) 1/3)) (fma.f64 (pow.f64 y 6) (fma.f64 (pow.f64 x 3) -1/24 (fma.f64 -1/2 (.f64 (pow.f64 x 3) 1/3) (fma.f64 -1/720 (pow.f64 x 3) (.f64 (pow.f64 x 3) -2/45)))) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (fma.f64 (pow.f64 y 6) (+.f64 (.f64 (pow.f64 x 3) -1/6) (fma.f64 (pow.f64 x 3) -1/24 (.f64 (pow.f64 x 3) -11/240))) (fma.f64 y (.f64 y (*.f64 (pow.f64 x 3) -3/2)) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (fma.f64 (pow.f64 y 6) (fma.f64 x (.f64 (.f64 x x) -19/90) (.f64 (pow.f64 x 3) -31/720)) (.f64 (+.f64 (.f64 (*.f64 -3/2 y) y) 1) (pow.f64 x 3))))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
	0.1b	(*.f64 x (cos.f64 y))
✓	0.6b	(cbrt.f64 (*.f64 x (cos.f64 y)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)

Compiler

Compiled 43 to 14 computations (67.4% saved)

series96.0ms (1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
83.0ms	y	@	inf	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)
3.0ms	y	@	0	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)
3.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)

rewrite58.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

638×	`pow1_binary64`
596×	`add-log-exp_binary64`
596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
581×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	166	14
2	1669	14

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-l_binary64`
652×	`associate-r_binary64`
581×	`fma-def_binary64`
426×	`distribute-rgt-out_binary64`
242×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	527
1	306	481
2	1000	416
3	5848	390

Stop Event

1×	node limit

Counts

76 → 71

Calls

Call 1

Inputs
(*.f64 (pow.f64 1 1/3) x)
(+.f64 (.f64 (pow.f64 1 1/3) x) (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) x)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) x))) (pow.f64 y 2)))
(+.f64 (.f64 (pow.f64 1 1/3) x) (+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) x)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) x))) (pow.f64 y 2)) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (+.f64 (.f64 1/18 (.f64 (pow.f64 1 1/3) x)) (.f64 (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3))) (pow.f64 (*.f64 1 x) 1/3)))))))
(+.f64 (.f64 (pow.f64 1 1/3) x) (+.f64 (.f64 (+.f64 (.f64 -1/6 (.f64 (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3))) (pow.f64 (.f64 1 x) 1/3))) (+.f64 (.f64 (pow.f64 (.f64 1 x) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 -1/720 x) (+.f64 (.f64 -1/3 (-.f64 (.f64 1/24 x) (.f64 1/12 x))) (.f64 -1/216 x))))) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))))) (+.f64 (.f64 1/3 (.f64 (-.f64 (.f64 -1/720 x) (+.f64 (.f64 -1/3 (-.f64 (.f64 1/24 x) (.f64 1/12 x))) (.f64 -1/216 x))) (pow.f64 1 1/3))) (.f64 -1/9 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x))))))) (pow.f64 y 6)) (+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) x)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) x))) (pow.f64 y 2)) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (+.f64 (.f64 1/18 (.f64 (pow.f64 1 1/3) x)) (.f64 (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3))) (pow.f64 (*.f64 1 x) 1/3))))))))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(pow.f64 x 1/3)
(+.f64 (pow.f64 x 1/3) (.f64 -1/6 (.f64 (pow.f64 (*.f64 1 x) 1/3) (pow.f64 y 2))))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (.f64 1/12 x))))) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2)))))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/3 (.f64 (.f64 (-.f64 (.f64 -1/720 x) (+.f64 (.f64 -1/3 (-.f64 (.f64 1/24 x) (.f64 1/12 x))) (.f64 -1/216 x))) (pow.f64 y 6)) (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (.f64 1/12 x))))) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2))))))
(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)

Outputs
(*.f64 (pow.f64 1 1/3) x)
x
(+.f64 (.f64 (pow.f64 1 1/3) x) (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) x)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) x))) (pow.f64 y 2)))
(+.f64 x (.f64 (.f64 x -1/2) (*.f64 y y)))
(fma.f64 (.f64 x -1/2) (.f64 y y) x)
(fma.f64 (.f64 x (.f64 y y)) -1/2 x)
(+.f64 (.f64 (pow.f64 1 1/3) x) (+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) x)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) x))) (pow.f64 y 2)) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (+.f64 (.f64 1/18 (.f64 (pow.f64 1 1/3) x)) (.f64 (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3))) (pow.f64 (*.f64 1 x) 1/3)))))))
(+.f64 x (fma.f64 (.f64 x -1/2) (.f64 y y) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/3 (.f64 x -1/24)) (fma.f64 1/18 x (.f64 (fma.f64 2/3 (.f64 (.f64 x -1/24) (cbrt.f64 (/.f64 1 x))) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x)))))))
(+.f64 x (fma.f64 (.f64 x -1/2) (.f64 y y) (.f64 (pow.f64 y 4) (fma.f64 1/3 (.f64 x -1/24) (fma.f64 (fma.f64 2/3 (.f64 (.f64 x -1/24) (cbrt.f64 (/.f64 1 x))) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x) (*.f64 x 1/18))))))
(fma.f64 x (.f64 (.f64 y y) -1/2) (fma.f64 (pow.f64 y 4) (fma.f64 (fma.f64 (cbrt.f64 (/.f64 1 x)) (.f64 x -1/36) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x) (fma.f64 x 1/18 (.f64 x -1/72))) x))
(fma.f64 x (.f64 (.f64 y y) -1/2) (fma.f64 (pow.f64 y 4) (fma.f64 (fma.f64 (cbrt.f64 (/.f64 1 x)) (.f64 x -1/36) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x) (.f64 x 1/24)) x))
(+.f64 (.f64 (pow.f64 1 1/3) x) (+.f64 (.f64 (+.f64 (.f64 -1/6 (.f64 (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3))) (pow.f64 (.f64 1 x) 1/3))) (+.f64 (.f64 (pow.f64 (.f64 1 x) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 -1/720 x) (+.f64 (.f64 -1/3 (-.f64 (.f64 1/24 x) (.f64 1/12 x))) (.f64 -1/216 x))))) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))))) (+.f64 (.f64 1/3 (.f64 (-.f64 (.f64 -1/720 x) (+.f64 (.f64 -1/3 (-.f64 (.f64 1/24 x) (.f64 1/12 x))) (.f64 -1/216 x))) (pow.f64 1 1/3))) (.f64 -1/9 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x))))))) (pow.f64 y 6)) (+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) x)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) x))) (pow.f64 y 2)) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (+.f64 (.f64 1/18 (.f64 (pow.f64 1 1/3) x)) (.f64 (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 x) 1/3) (-.f64 (.f64 1/24 x) (.f64 1/12 x)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3))) (pow.f64 (*.f64 1 x) 1/3))))))))
(+.f64 x (fma.f64 (fma.f64 -1/6 (.f64 (fma.f64 2/3 (.f64 (.f64 x -1/24) (cbrt.f64 (/.f64 1 x))) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x)) (fma.f64 (cbrt.f64 x) (fma.f64 2/3 (.f64 (cbrt.f64 (/.f64 1 x)) (-.f64 (.f64 x -1/720) (fma.f64 -1/3 (.f64 x -1/24) (.f64 x -1/216)))) (.f64 (.f64 (.f64 x -1/24) (cbrt.f64 (/.f64 1 x))) -1/9)) (fma.f64 1/3 (.f64 1 (-.f64 (.f64 x -1/720) (fma.f64 -1/3 (.f64 x -1/24) (.f64 x -1/216)))) (.f64 -1/9 (.f64 x -1/24))))) (pow.f64 y 6) (fma.f64 (.f64 x -1/2) (.f64 y y) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/3 (.f64 x -1/24)) (fma.f64 1/18 x (.f64 (fma.f64 2/3 (.f64 (.f64 x -1/24) (cbrt.f64 (/.f64 1 x))) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x))))))))
(+.f64 x (fma.f64 (+.f64 (fma.f64 1/3 (-.f64 (.f64 x -1/720) (fma.f64 x -1/216 (.f64 x 1/72))) (.f64 (.f64 -1/9 x) -1/24)) (.f64 (cbrt.f64 x) (+.f64 (.f64 -1/6 (fma.f64 2/3 (.f64 (.f64 x -1/24) (cbrt.f64 (/.f64 1 x))) (.f64 1/36 (cbrt.f64 (.f64 x x))))) (fma.f64 2/3 (.f64 (cbrt.f64 (/.f64 1 x)) (-.f64 (.f64 x -1/720) (fma.f64 x -1/216 (.f64 x 1/72)))) (.f64 (cbrt.f64 (/.f64 1 x)) (.f64 (.f64 -1/9 x) -1/24)))))) (pow.f64 y 6) (fma.f64 (.f64 x -1/2) (.f64 y y) (.f64 (pow.f64 y 4) (fma.f64 1/3 (.f64 x -1/24) (fma.f64 (fma.f64 2/3 (.f64 (.f64 x -1/24) (cbrt.f64 (/.f64 1 x))) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x) (*.f64 x 1/18)))))))
(fma.f64 (fma.f64 (cbrt.f64 x) (fma.f64 -1/6 (fma.f64 (cbrt.f64 (/.f64 1 x)) (.f64 x -1/36) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 (.f64 2/3 (+.f64 (.f64 x 7/2160) (.f64 x -1/72))) (.f64 x 1/216)))) (fma.f64 1/3 (+.f64 (.f64 x 7/2160) (.f64 x -1/72)) (.f64 x 1/216))) (pow.f64 y 6) (fma.f64 x (.f64 (.f64 y y) -1/2) (fma.f64 (pow.f64 y 4) (fma.f64 (fma.f64 (cbrt.f64 (/.f64 1 x)) (.f64 x -1/36) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x) (fma.f64 x 1/18 (*.f64 x -1/72))) x)))
(fma.f64 (fma.f64 (cbrt.f64 x) (fma.f64 -1/6 (fma.f64 (cbrt.f64 (/.f64 1 x)) (.f64 x -1/36) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 (.f64 2/3 (.f64 x -23/2160)) (.f64 x 1/216)))) (fma.f64 1/3 (.f64 x -23/2160) (.f64 x 1/216))) (pow.f64 y 6) (fma.f64 x (.f64 (.f64 y y) -1/2) (fma.f64 (pow.f64 y 4) (fma.f64 (fma.f64 (cbrt.f64 (/.f64 1 x)) (.f64 x -1/36) (.f64 1/36 (cbrt.f64 (.f64 x x)))) (cbrt.f64 x) (*.f64 x 1/24)) x)))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.f64 x (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.f64 x (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.f64 x (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.f64 x (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.f64 x (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.f64 x (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.f64 x (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 (cos.f64 y) x))
(.f64 1 (.f64 x (cos.f64 y)))
(*.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 (*.f64 1 x) 1/3) (pow.f64 y 2))))
(+.f64 (cbrt.f64 x) (.f64 (.f64 -1/6 (cbrt.f64 x)) (*.f64 y y)))
(fma.f64 -1/6 (.f64 (.f64 y y) (cbrt.f64 x)) (cbrt.f64 x))
(fma.f64 (.f64 y y) (.f64 -1/6 (cbrt.f64 x)) (cbrt.f64 x))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (.f64 1/12 x))))) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2)))))
(+.f64 (cbrt.f64 x) (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (pow.f64 y 4) (.f64 x -1/24))) (.f64 (.f64 -1/6 (cbrt.f64 x)) (*.f64 y y))))
(+.f64 (cbrt.f64 x) (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 x (.f64 -1/24 (pow.f64 y 4)))) (.f64 -1/6 (.f64 (*.f64 y y) (cbrt.f64 x)))))
(fma.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (pow.f64 y 4) (.f64 x -1/72)) (fma.f64 (.f64 y y) (*.f64 -1/6 (cbrt.f64 x)) (cbrt.f64 x)))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/3 (.f64 (.f64 (-.f64 (.f64 -1/720 x) (+.f64 (.f64 -1/3 (-.f64 (.f64 1/24 x) (.f64 1/12 x))) (.f64 -1/216 x))) (pow.f64 y 6)) (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (.f64 1/12 x))))) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2))))))
(+.f64 (cbrt.f64 x) (fma.f64 1/3 (.f64 (-.f64 (.f64 x -1/720) (fma.f64 -1/3 (.f64 x -1/24) (.f64 x -1/216))) (.f64 (pow.f64 y 6) (cbrt.f64 (/.f64 1 (.f64 x x))))) (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (pow.f64 y 4) (.f64 x -1/24))) (.f64 (.f64 -1/6 (cbrt.f64 x)) (*.f64 y y)))))
(+.f64 (.f64 1/3 (+.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (-.f64 (.f64 x -1/720) (fma.f64 x -1/216 (.f64 x 1/72))) (pow.f64 y 6))) (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 x (.f64 -1/24 (pow.f64 y 4)))))) (fma.f64 -1/6 (.f64 (.f64 y y) (cbrt.f64 x)) (cbrt.f64 x)))
(fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (+.f64 (.f64 (+.f64 (.f64 x 7/2160) (.f64 x -1/72)) (pow.f64 y 6)) (.f64 x (.f64 (pow.f64 y 4) -1/24)))) (fma.f64 (.f64 y y) (*.f64 -1/6 (cbrt.f64 x)) (cbrt.f64 x)))
(fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (+.f64 (.f64 x (.f64 (pow.f64 y 4) -1/24)) (.f64 (.f64 x -23/2160) (pow.f64 y 6)))) (fma.f64 (.f64 y y) (.f64 -1/6 (cbrt.f64 x)) (cbrt.f64 x)))
(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)))

eval150.0ms (1.5%)

Compiler: Compiled 9178 to 3807 computations (58.5% saved)

prune131.0ms (1.3%)

Pruning

23 alts after pruning (18 fresh and 5 done)

	Pruned	Kept	Total
New	555	11	566
Fresh	8	7	15
Picked	0	1	1
Done	1	4	5
Total	564	23	587

Error

0.0b

Counts

587 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	31.2b	(fma.f64 z y x)
✓	0.9b	(+.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
▶	29.6b	(fma.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) (.f64 x (cos.f64 y)))
	38.5b	x
	42.5b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 y z))
	0.6b	(fma.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (.f64 x (cos.f64 y)))
	30.2b	(+.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))) (.f64 z (sin.f64 y)))
	27.3b	(+.f64 (.f64 x (pow.f64 (sqrt.f64 (cos.f64 y)) 2)) (.f64 y z))
✓	31.2b	(+.f64 (*.f64 y z) x)
▶	0.2b	(+.f64 (.f64 x (log1p.f64 (expm1.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
	39.7b	(*.f64 z (sin.f64 y))
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))
	18.9b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
	24.1b	(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 y z))
	31.5b	(+.f64 (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) (*.f64 z (sin.f64 y)))
	24.2b	(*.f64 (cos.f64 y) x)
▶	0.2b	(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
▶	15.7b	(+.f64 x (*.f64 z (sin.f64 y)))
▶	54.5b	(*.f64 y z)
	2.9b	(fma.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) z) (.f64 x (cos.f64 y)))
	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
✓	29.9b	(+.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))

Compiler

Compiled 501 to 345 computations (31.1% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 38 to 10 computations (73.7% saved)

series7.0ms (0.1%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(expm1.f64 (cos.f64 y))
1.0ms	y	@	inf	(expm1.f64 (cos.f64 y))
1.0ms	y	@	-inf	(expm1.f64 (cos.f64 y))
1.0ms	y	@	0	(log1p.f64 (expm1.f64 (cos.f64 y)))
0.0ms	y	@	0	(*.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))))

rewrite99.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`pow1_binary64`
518×	`add-sqr-sqrt_binary64`
498×	`expm1-log1p-u_binary64`
497×	`add-log-exp_binary64`
497×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	119	14
2	1356	14

Stop Event

1×	node limit

Counts

3 → 45

Calls

Call 1

Inputs
(expm1.f64 (cos.f64 y))
(log1p.f64 (expm1.f64 (cos.f64 y)))
(*.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))))

Outputs

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

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

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

simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
522×	`distribute-rgt-neg-in_binary64`
435×	`cancel-sign-sub-inv_binary64`
382×	`distribute-lft-neg-in_binary64`
360×	`unsub-neg_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	52	392
1	136	380
2	365	365
3	1219	359
4	1925	356
5	3134	354
6	5243	354
7	7578	354

Stop Event

1×	node limit

Counts

93 → 69

Calls

Call 1

Inputs
(-.f64 (E.f64) 1)
(-.f64 (+.f64 (E.f64) (.f64 -1/2 (.f64 (E.f64) (pow.f64 y 2)))) 1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 y 2))) (.f64 1/6 (.f64 (E.f64) (pow.f64 y 4))))) 1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 y 2))) (+.f64 (.f64 -31/720 (.f64 (E.f64) (pow.f64 y 6))) (.f64 1/6 (.f64 (E.f64) (pow.f64 y 4)))))) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
1
(+.f64 1 (*.f64 -1/2 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (.f64 1/24 (pow.f64 y 4))))
(+.f64 (.f64 -1/720 (pow.f64 y 6)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (*.f64 1/24 (pow.f64 y 4)))))
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(*.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)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) 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)

Outputs
(-.f64 (E.f64) 1)
(expm1.f64 1)
(-.f64 (+.f64 (E.f64) (.f64 -1/2 (.f64 (E.f64) (pow.f64 y 2)))) 1)
(+.f64 (+.f64 (E.f64) (.f64 -1/2 (.f64 (E.f64) (*.f64 y y)))) -1)
(+.f64 (.f64 (.f64 y y) (*.f64 (E.f64) -1/2)) (expm1.f64 1))
(fma.f64 (.f64 y y) (.f64 (E.f64) -1/2) (expm1.f64 1))
(fma.f64 (fma.f64 -1/2 (*.f64 y y) 1) (E.f64) -1)
(fma.f64 (E.f64) (fma.f64 -1/2 (*.f64 y y) 1) -1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 y 2))) (.f64 1/6 (.f64 (E.f64) (pow.f64 y 4))))) 1)
(+.f64 (+.f64 (E.f64) (fma.f64 -1/2 (.f64 (E.f64) (.f64 y y)) (.f64 1/6 (.f64 (E.f64) (pow.f64 y 4))))) -1)
(+.f64 (fma.f64 1/6 (.f64 (E.f64) (pow.f64 y 4)) (.f64 (.f64 y y) (.f64 (E.f64) -1/2))) (expm1.f64 1))
(+.f64 (expm1.f64 1) (.f64 (E.f64) (+.f64 (.f64 1/6 (pow.f64 y 4)) (.f64 -1/2 (.f64 y y)))))
(+.f64 (.f64 (E.f64) (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (*.f64 1/6 (pow.f64 y 4)))) -1)
(fma.f64 (E.f64) (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (.f64 1/6 (pow.f64 y 4))) -1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 y 2))) (+.f64 (.f64 -31/720 (.f64 (E.f64) (pow.f64 y 6))) (.f64 1/6 (.f64 (E.f64) (pow.f64 y 4)))))) 1)
(+.f64 (+.f64 (E.f64) (fma.f64 -1/2 (.f64 (E.f64) (.f64 y y)) (fma.f64 -31/720 (.f64 (E.f64) (pow.f64 y 6)) (.f64 1/6 (*.f64 (E.f64) (pow.f64 y 4)))))) -1)
(+.f64 (fma.f64 -1/2 (.f64 (E.f64) (.f64 y y)) (fma.f64 1/6 (.f64 (E.f64) (pow.f64 y 4)) (.f64 (pow.f64 y 6) (*.f64 (E.f64) -31/720)))) (expm1.f64 1))
(+.f64 (expm1.f64 1) (fma.f64 (E.f64) (.f64 -1/2 (.f64 y y)) (.f64 (E.f64) (+.f64 (.f64 1/6 (pow.f64 y 4)) (*.f64 -31/720 (pow.f64 y 6))))))
(+.f64 (expm1.f64 1) (.f64 (E.f64) (+.f64 (.f64 y (+.f64 (.f64 1/6 (pow.f64 y 3)) (.f64 -1/2 y))) (*.f64 -31/720 (pow.f64 y 6)))))
(+.f64 (.f64 (E.f64) (+.f64 (.f64 -31/720 (pow.f64 y 6)) (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (.f64 1/6 (pow.f64 y 4))))) -1)
(fma.f64 (E.f64) (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (+.f64 (.f64 -31/720 (pow.f64 y 6)) (*.f64 1/6 (pow.f64 y 4)))) -1)
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
(-.f64 (exp.f64 (cos.f64 y)) 1)
(expm1.f64 (cos.f64 y))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 y 2)))
(+.f64 1 (.f64 -1/2 (.f64 y y)))
(fma.f64 -1/2 (*.f64 y y) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (.f64 1/24 (pow.f64 y 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 y y) (.f64 (pow.f64 y 4) 1/24)))
(+.f64 (fma.f64 -1/2 (.f64 y y) 1) (.f64 (pow.f64 y 4) 1/24))
(fma.f64 -1/2 (*.f64 y y) (fma.f64 (pow.f64 y 4) 1/24 1))
(fma.f64 (pow.f64 y 4) 1/24 (fma.f64 -1/2 (*.f64 y y) 1))
(+.f64 (.f64 -1/720 (pow.f64 y 6)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (*.f64 1/24 (pow.f64 y 4)))))
(fma.f64 -1/720 (pow.f64 y 6) (+.f64 1 (fma.f64 -1/2 (.f64 y y) (.f64 (pow.f64 y 4) 1/24))))
(fma.f64 (pow.f64 y 6) -1/720 (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (.f64 (pow.f64 y 4) 1/24)))
(fma.f64 (pow.f64 y 6) -1/720 (fma.f64 -1/2 (*.f64 y y) (fma.f64 (pow.f64 y 4) 1/24 1)))
(fma.f64 (pow.f64 y 6) -1/720 (fma.f64 (pow.f64 y 4) 1/24 (fma.f64 -1/2 (*.f64 y y) 1)))
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(*.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)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 (.f64 y y) x) x)
(fma.f64 -1/2 (.f64 (.f64 x y) y) x)
(.f64 (fma.f64 -1/2 (.f64 y y) 1) x)
(fma.f64 (.f64 y y) (.f64 -1/2 x) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 (pow.f64 y 4) x) (fma.f64 -1/2 (.f64 (*.f64 y y) x) x))
(+.f64 x (.f64 x (fma.f64 -1/2 (.f64 y y) (*.f64 (pow.f64 y 4) 1/24))))
(.f64 x (fma.f64 -1/2 (.f64 y y) (fma.f64 (pow.f64 y 4) 1/24 1)))
(.f64 (fma.f64 -1/2 (.f64 y y) (fma.f64 (pow.f64 y 4) 1/24 1)) x)
(.f64 (fma.f64 (pow.f64 y 4) 1/24 (fma.f64 -1/2 (.f64 y y) 1)) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 (pow.f64 y 6) x) (fma.f64 1/24 (.f64 (pow.f64 y 4) x) (fma.f64 -1/2 (.f64 (.f64 y y) x) x)))
(fma.f64 -1/720 (.f64 (pow.f64 y 6) x) (+.f64 x (.f64 x (fma.f64 -1/2 (.f64 y y) (.f64 (pow.f64 y 4) 1/24)))))
(+.f64 x (.f64 x (fma.f64 (pow.f64 y 6) -1/720 (fma.f64 -1/2 (.f64 y y) (*.f64 (pow.f64 y 4) 1/24)))))
(.f64 x (fma.f64 (pow.f64 y 6) -1/720 (fma.f64 -1/2 (.f64 y y) (fma.f64 (pow.f64 y 4) 1/24 1))))
(.f64 (fma.f64 (pow.f64 y 6) -1/720 (fma.f64 -1/2 (.f64 y y) (fma.f64 (pow.f64 y 4) 1/24 1))) x)
(.f64 (fma.f64 (pow.f64 y 6) -1/720 (fma.f64 (pow.f64 y 4) 1/24 (fma.f64 -1/2 (.f64 y y) 1))) 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)

localize7.0ms (0.1%)

Compiler: Compiled 8 to 4 computations (50% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 18 to 6 computations (66.7% saved)

series6.0ms (0.1%)

Counts

1 → 27

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	z	@	inf	(+.f64 x (*.f64 z (sin.f64 y)))
1.0ms	x	@	0	(+.f64 x (*.f64 z (sin.f64 y)))
0.0ms	y	@	0	(+.f64 x (*.f64 z (sin.f64 y)))
0.0ms	x	@	inf	(+.f64 x (*.f64 z (sin.f64 y)))
0.0ms	y	@	-inf	(+.f64 x (*.f64 z (sin.f64 y)))

rewrite80.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`pow1_binary64`
747×	`add-log-exp_binary64`
747×	`log1p-expm1-u_binary64`
747×	`expm1-log1p-u_binary64`
730×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	147	7
2	2003	7

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify170.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1295×	`fma-def_binary64`
788×	`sqr-pow_binary64`
544×	`associate-l_binary64`
487×	`*-commutative_binary64`
448×	`cube-prod_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	186
1	65	186
2	152	182
3	380	179
4	995	177
5	2360	177
6	2811	177
7	3453	177
8	3569	177
9	3741	177
10	3960	177
11	4946	177
12	5406	177
13	6006	177
14	6759	177
15	7693	177

Stop Event

1×	node limit

Counts

62 → 44

Calls

Call 1

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

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

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f64 (cos.f64 y))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(*.f64 x (log.f64 (exp.f64 (cos.f64 y))))
✓	0.3b	(log.f64 (exp.f64 (cos.f64 y)))

Compiler

Compiled 38 to 10 computations (73.7% saved)

series7.0ms (0.1%)

Counts

3 → 40

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	(log.f64 (exp.f64 (cos.f64 y)))
1.0ms	y	@	0	(exp.f64 (cos.f64 y))
0.0ms	y	@	0	(*.f64 x (log.f64 (exp.f64 (cos.f64 y))))
0.0ms	y	@	inf	(log.f64 (exp.f64 (cos.f64 y)))
0.0ms	x	@	0	(*.f64 x (log.f64 (exp.f64 (cos.f64 y))))

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

531×	`pow1_binary64`
504×	`add-sqr-sqrt_binary64`
484×	`log1p-expm1-u_binary64`
484×	`expm1-log1p-u_binary64`
483×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	119	14
2	1330	14

Stop Event

1×	node limit

Counts

3 → 49

Calls

Call 1

Inputs
(log.f64 (exp.f64 (cos.f64 y)))
(*.f64 x (log.f64 (exp.f64 (cos.f64 y))))
(exp.f64 (cos.f64 y))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 y))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cos.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cos.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (cbrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 y)) (sqrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cos.f64 y)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 y)))))))

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

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

simplify174.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1604×	`fma-def_binary64`
820×	`unswap-sqr_binary64`
612×	`sqr-pow_binary64`
454×	`cube-prod_binary64`
356×	`pow-sqr_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	46	334
1	119	328
2	324	311
3	1061	307
4	1622	307
5	2083	307
6	2216	307
7	2342	307
8	2476	304
9	3991	304
10	4233	304
11	5933	304
12	6496	304
13	7149	304
14	7882	304

Stop Event

1×	node limit

Counts

89 → 72

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (.f64 1/24 (pow.f64 y 4))))
(+.f64 (.f64 -1/720 (pow.f64 y 6)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (*.f64 1/24 (pow.f64 y 4)))))
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(*.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)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) 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)
(exp.f64 1)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) (exp.f64 1))) (exp.f64 1))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) (exp.f64 1))) (+.f64 (.f64 1/6 (.f64 (pow.f64 y 4) (exp.f64 1))) (exp.f64 1)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) (exp.f64 1))) (+.f64 (.f64 1/6 (.f64 (pow.f64 y 4) (exp.f64 1))) (+.f64 (.f64 -31/720 (.f64 (pow.f64 y 6) (exp.f64 1))) (exp.f64 1))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 y 2)))
(+.f64 1 (.f64 -1/2 (.f64 y y)))
(fma.f64 -1/2 (*.f64 y y) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (.f64 1/24 (pow.f64 y 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 y y) (.f64 1/24 (pow.f64 y 4))))
(+.f64 (fma.f64 -1/2 (.f64 y y) 1) (.f64 1/24 (pow.f64 y 4)))
(fma.f64 -1/2 (*.f64 y y) (fma.f64 1/24 (pow.f64 y 4) 1))
(+.f64 (.f64 -1/720 (pow.f64 y 6)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 y 2)) (*.f64 1/24 (pow.f64 y 4)))))
(fma.f64 -1/720 (pow.f64 y 6) (+.f64 1 (fma.f64 -1/2 (.f64 y y) (.f64 1/24 (pow.f64 y 4)))))
(+.f64 (fma.f64 -1/2 (.f64 y y) (.f64 1/24 (pow.f64 y 4))) (fma.f64 -1/720 (pow.f64 y 6) 1))
(fma.f64 -1/720 (pow.f64 y 6) (fma.f64 -1/2 (*.f64 y y) (fma.f64 1/24 (pow.f64 y 4) 1)))
(fma.f64 -1/2 (*.f64 y y) (fma.f64 -1/720 (pow.f64 y 6) (fma.f64 1/24 (pow.f64 y 4) 1)))
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(cos.f64 y)
(*.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)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 (.f64 y y) x) x)
(.f64 (fma.f64 -1/2 (.f64 y y) 1) x)
(fma.f64 (.f64 y y) (.f64 -1/2 x) x)
(fma.f64 y (.f64 y (.f64 -1/2 x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 (pow.f64 y 4) x) (fma.f64 -1/2 (.f64 (*.f64 y y) x) x))
(+.f64 x (.f64 x (fma.f64 -1/2 (.f64 y y) (*.f64 1/24 (pow.f64 y 4)))))
(.f64 x (fma.f64 -1/2 (.f64 y y) (fma.f64 1/24 (pow.f64 y 4) 1)))
(.f64 (fma.f64 -1/2 (.f64 y y) (fma.f64 1/24 (pow.f64 y 4) 1)) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 (pow.f64 y 6) x) (fma.f64 1/24 (.f64 (pow.f64 y 4) x) (fma.f64 -1/2 (.f64 (.f64 y y) x) x)))
(fma.f64 -1/720 (.f64 (pow.f64 y 6) x) (+.f64 x (.f64 x (fma.f64 -1/2 (.f64 y y) (.f64 1/24 (pow.f64 y 4))))))
(+.f64 x (.f64 x (fma.f64 -1/720 (pow.f64 y 6) (fma.f64 -1/2 (.f64 y y) (*.f64 1/24 (pow.f64 y 4))))))
(.f64 x (fma.f64 -1/720 (pow.f64 y 6) (fma.f64 -1/2 (.f64 y y) (fma.f64 1/24 (pow.f64 y 4) 1))))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 (.f64 y y) (fma.f64 y (*.f64 y 1/24) -1/2))) x)
(.f64 x (fma.f64 -1/2 (.f64 y y) (fma.f64 -1/720 (pow.f64 y 6) (fma.f64 1/24 (pow.f64 y 4) 1))))
(*.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)
(exp.f64 1)
(E.f64)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) (exp.f64 1))) (exp.f64 1))
(fma.f64 -1/2 (.f64 (.f64 y y) (E.f64)) (E.f64))
(.f64 (fma.f64 -1/2 (.f64 y y) 1) (E.f64))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) (exp.f64 1))) (+.f64 (.f64 1/6 (.f64 (pow.f64 y 4) (exp.f64 1))) (exp.f64 1)))
(fma.f64 -1/2 (.f64 (.f64 y y) (E.f64)) (fma.f64 1/6 (*.f64 (pow.f64 y 4) (E.f64)) (E.f64)))
(fma.f64 -1/2 (.f64 y (.f64 y (E.f64))) (fma.f64 (*.f64 (pow.f64 y 4) 1/6) (E.f64) (E.f64)))
(fma.f64 (E.f64) (fma.f64 -1/2 (.f64 y y) (.f64 (pow.f64 y 4) 1/6)) (E.f64))
(.f64 (E.f64) (fma.f64 y (fma.f64 1/6 (pow.f64 y 3) (.f64 -1/2 y)) 1))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) (exp.f64 1))) (+.f64 (.f64 1/6 (.f64 (pow.f64 y 4) (exp.f64 1))) (+.f64 (.f64 -31/720 (.f64 (pow.f64 y 6) (exp.f64 1))) (exp.f64 1))))
(fma.f64 -1/2 (.f64 (.f64 y y) (E.f64)) (fma.f64 1/6 (.f64 (pow.f64 y 4) (E.f64)) (fma.f64 -31/720 (.f64 (pow.f64 y 6) (E.f64)) (E.f64))))
(+.f64 (.f64 (E.f64) (+.f64 (.f64 (pow.f64 y 4) 1/6) (.f64 (pow.f64 y 6) -31/720))) (.f64 (fma.f64 -1/2 (*.f64 y y) 1) (E.f64)))
(fma.f64 (E.f64) (fma.f64 (pow.f64 y 4) 1/6 (.f64 (pow.f64 y 6) -31/720)) (.f64 (fma.f64 -1/2 (*.f64 y y) 1) (E.f64)))
(.f64 (E.f64) (+.f64 (fma.f64 (pow.f64 y 6) -31/720 1) (fma.f64 -1/2 (.f64 y y) (*.f64 (pow.f64 y 4) 1/6))))
(.f64 (E.f64) (fma.f64 -1/2 (.f64 y y) (fma.f64 (pow.f64 y 4) 1/6 (fma.f64 (pow.f64 y 6) -31/720 1))))
(.f64 (E.f64) (fma.f64 y (fma.f64 1/6 (pow.f64 y 3) (.f64 -1/2 y)) (fma.f64 (pow.f64 y 6) -31/720 1)))

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 33 to 9 computations (72.7% saved)

series18.0ms (0.2%)

Counts

2 → 37

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	z	@	-inf	(fma.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) (.f64 x (cos.f64 y)))
2.0ms	z	@	inf	(*.f64 (sin.f64 y) (sqrt.f64 z))
2.0ms	z	@	inf	(fma.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) (.f64 x (cos.f64 y)))
1.0ms	z	@	0	(*.f64 (sin.f64 y) (sqrt.f64 z))
1.0ms	z	@	-inf	(*.f64 (sin.f64 y) (sqrt.f64 z))

rewrite93.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

931×	`pow1_binary64`
850×	`add-log-exp_binary64`
850×	`log1p-expm1-u_binary64`
850×	`expm1-log1p-u_binary64`
828×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	196	22
2	2329	22

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

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

Outputs

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

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

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
864×	`distribute-lft-out_binary64`
532×	`distribute-rgt-in_binary64`
420×	`associate-l_binary64`
409×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	434
1	125	424
2	327	405
3	969	403
4	2988	403
5	3722	403
6	5990	403
7	6693	403
8	7073	403
9	7638	403

Stop Event

1×	node limit

Counts

71 → 55

Calls

Call 1

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

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

eval95.0ms (1%)

Compiler: Compiled 6537 to 2356 computations (64% saved)

prune91.0ms (0.9%)

Pruning

23 alts after pruning (14 fresh and 9 done)

	Pruned	Kept	Total
New	422	8	430
Fresh	7	6	13
Picked	1	0	1
Done	0	9	9
Total	430	23	453

Error

0.0b

Counts

453 → 23

Alt Table

Click to see full alt table

Status	Error	Program
▶	39.7b	(*.f64 z (sin.f64 y))
▶	0.2b	(+.f64 (.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1)) (.f64 z (sin.f64 y)))
	24.1b	(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 y z))
✓	0.9b	(+.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
	37.3b	(fma.f64 (*.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) x)
	0.6b	(fma.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (.f64 x (cos.f64 y)))
▶	30.2b	(+.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))) (.f64 z (sin.f64 y)))
✓	31.2b	(+.f64 (*.f64 y z) x)
✓	0.2b	(+.f64 (.f64 x (log1p.f64 (expm1.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
	38.5b	x
✓	29.9b	(+.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))
	31.2b	(fma.f64 z y x)
✓	0.2b	(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	15.7b	(+.f64 x (*.f64 z (sin.f64 y)))
	16.1b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
✓	54.5b	(*.f64 y z)
	2.9b	(fma.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) z) (.f64 x (cos.f64 y)))
	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
▶	42.5b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 y z))
▶	31.5b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))
	24.2b	(*.f64 (cos.f64 y) x)

Compiler

Compiled 442 to 309 computations (30.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(*.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1))
✓	0.3b	(+.f64 1 (cos.f64 y))
✓	0.4b	(-.f64 (+.f64 1 (cos.f64 y)) 1)

Compiler

Compiled 46 to 24 computations (47.8% saved)

series3.0ms (0%)

Counts

3 → 40

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(-.f64 (+.f64 1 (cos.f64 y)) 1)
0.0ms	y	@	0	(+.f64 1 (cos.f64 y))
0.0ms	y	@	inf	(+.f64 1 (cos.f64 y))
0.0ms	y	@	0	(*.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1))
0.0ms	y	@	-inf	(+.f64 1 (cos.f64 y))

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`pow1_binary64`
790×	`add-log-exp_binary64`
790×	`log1p-expm1-u_binary64`
790×	`expm1-log1p-u_binary64`
776×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	173	15
2	2412	15

Stop Event

1×	node limit

Counts

3 → 93

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (cos.f64 y)) 1)
(+.f64 1 (cos.f64 y))
(*.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (cos.f64 y) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (cos.f64 y) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (cos.f64 y) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (cos.f64 y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (cos.f64 y) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cos.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (cbrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 y)) (sqrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 2) (+.f64 (cos.f64 y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (cos.f64 y) 2) (cos.f64 y)) (/.f64 1 (+.f64 (cos.f64 y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1 (cos.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 1 (cos.f64 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 2) (+.f64 (cos.f64 y) 2)) (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (cos.f64 y) 2) (*.f64 (+.f64 (cos.f64 y) 2) (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 2) (+.f64 (cos.f64 y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 2) (-.f64 1 (*.f64 (+.f64 1 (cos.f64 y)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (cos.f64 y) 2) (cos.f64 y)) (+.f64 (cos.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (cos.f64 y) 2) (cos.f64 y)) (-.f64 (+.f64 1 (cos.f64 y)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (cos.f64 y)) 2) (+.f64 (cos.f64 y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (+.f64 (cos.f64 y) 2) (cos.f64 y))) (neg.f64 (+.f64 (cos.f64 y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (cos.f64 y) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (cos.f64 y) -1) (+.f64 (cos.f64 y) -1)) (+.f64 (cos.f64 y) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (cos.f64 y) -1) (+.f64 (cos.f64 y) -1))) (-.f64 1 (+.f64 (cos.f64 y) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cos.f64 y)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (cos.f64 y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 y))) 2) (cbrt.f64 (+.f64 1 (cos.f64 y))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (cos.f64 y))) (sqrt.f64 (+.f64 1 (cos.f64 y))) -1)))))

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

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

simplify126.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
579×	`distribute-rgt-out_binary64`
459×	`*-commutative_binary64`
449×	`associate-l_binary64`
442×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	312
1	85	306
2	230	293
3	727	291
4	2781	291
5	5168	291
6	5437	291
7	5797	291
8	6482	291
9	7395	291
10	7984	291

Stop Event

1×	node limit

Counts

133 → 115

Calls

Call 1

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

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

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))

Compiler

Compiled 11 to 5 computations (54.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(pow.f64 (*.f64 z (sin.f64 y)) 3)
✓	34.3b	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))

Compiler

Compiled 35 to 15 computations (57.1% saved)

series11.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	z	@	-inf	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
1.0ms	y	@	0	(pow.f64 (*.f64 z (sin.f64 y)) 3)
1.0ms	y	@	-inf	(pow.f64 (*.f64 z (sin.f64 y)) 3)
1.0ms	y	@	inf	(pow.f64 (*.f64 z (sin.f64 y)) 3)
1.0ms	z	@	-inf	(pow.f64 (*.f64 z (sin.f64 y)) 3)

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

979×	`pow1_binary64`
914×	`add-log-exp_binary64`
914×	`log1p-expm1-u_binary64`
914×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	217	22
2	2534	22

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

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

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

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

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

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-def_binary64`
490×	`distribute-rgt-in_binary64`
484×	`distribute-lft-in_binary64`
476×	`associate-l_binary64`
434×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	84	905
1	266	887
2	931	836
3	4709	836
4	7315	833
5	7450	833
6	7634	833
7	7864	832

Stop Event

1×	node limit

Counts

176 → 121

Calls

Call 1

Inputs
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(*.f64 y z)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 y 3) (pow.f64 z 3))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (pow.f64 z 3)) (.f64 -1/6 (pow.f64 z 3))) (pow.f64 y 5)) (.f64 (pow.f64 y 3) (pow.f64 z 3)))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (pow.f64 z 3)) (.f64 -1/6 (pow.f64 z 3))) (pow.f64 y 5)) (+.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 z 2)) (.f64 1/60 (pow.f64 z 2))) z) (+.f64 (.f64 1/18 (pow.f64 z 3)) (.f64 1/120 (pow.f64 z 3)))))))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (pow.f64 z 3)) (.f64 -1/6 (pow.f64 z 3))) (pow.f64 y 5)) (+.f64 (.f64 (pow.f64 y 9) (+.f64 (.f64 -1/6 (.f64 (+.f64 (.f64 1/36 (pow.f64 z 2)) (.f64 1/60 (pow.f64 z 2))) z)) (+.f64 (.f64 z (+.f64 (.f64 -1/360 (pow.f64 z 2)) (.f64 -1/2520 (pow.f64 z 2)))) (+.f64 (.f64 -1/5040 (pow.f64 z 3)) (.f64 -1/360 (pow.f64 z 3)))))) (+.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 z 2)) (.f64 1/60 (pow.f64 z 2))) z) (+.f64 (.f64 1/18 (pow.f64 z 3)) (.f64 1/120 (pow.f64 z 3))))))))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 x (*.f64 z (sin.f64 y)))
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 x (*.f64 z (sin.f64 y)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(+.f64 (.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y)))) x)
(+.f64 (.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y)))) x)
(+.f64 (.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y)))) x)
x
(+.f64 (*.f64 y z) x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (*.f64 (pow.f64 y 3) z)) x))
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 1/120 (*.f64 (pow.f64 y 5) z)) x)))
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)

Outputs
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(neg.f64 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 z)))
(.f64 z (.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(neg.f64 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 z)))
(.f64 z (.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(neg.f64 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 z)))
(.f64 z (.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(neg.f64 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 z)))
(.f64 z (.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 z y))
(.f64 z (+.f64 y (.f64 -1/6 (pow.f64 y 3))))
(*.f64 z (fma.f64 -1/6 (pow.f64 y 3) y))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (.f64 (*.f64 1/120 (pow.f64 y 5)) z)))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 z (+.f64 (*.f64 1/120 (pow.f64 y 5)) y)))
(.f64 z (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (.f64 1/120 (pow.f64 y 5))))
(.f64 z (+.f64 (.f64 1/120 (pow.f64 y 5)) (fma.f64 -1/6 (pow.f64 y 3) y)))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (fma.f64 -1/5040 (.f64 z (pow.f64 y 7)) (.f64 (.f64 1/120 (pow.f64 y 5)) z))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 z y (.f64 z (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))))
(.f64 z (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (fma.f64 -1/5040 (pow.f64 y 7) (.f64 1/120 (pow.f64 y 5)))))
(.f64 z (+.f64 (fma.f64 -1/5040 (pow.f64 y 7) (.f64 1/120 (pow.f64 y 5))) (fma.f64 -1/6 (pow.f64 y 3) y)))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 y 3) (pow.f64 z 3))
(pow.f64 (*.f64 z y) 3)
(+.f64 (.f64 (+.f64 (.f64 -1/3 (pow.f64 z 3)) (.f64 -1/6 (pow.f64 z 3))) (pow.f64 y 5)) (.f64 (pow.f64 y 3) (pow.f64 z 3)))
(fma.f64 (.f64 (pow.f64 z 3) -1/2) (pow.f64 y 5) (.f64 (pow.f64 y 3) (pow.f64 z 3)))
(fma.f64 (pow.f64 y 3) (pow.f64 z 3) (.f64 (pow.f64 y 5) (.f64 (pow.f64 z 3) -1/2)))
(.f64 (pow.f64 z 3) (+.f64 (pow.f64 y 3) (.f64 (pow.f64 y 5) -1/2)))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (pow.f64 z 3)) (.f64 -1/6 (pow.f64 z 3))) (pow.f64 y 5)) (+.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 z 2)) (.f64 1/60 (pow.f64 z 2))) z) (+.f64 (.f64 1/18 (pow.f64 z 3)) (.f64 1/120 (pow.f64 z 3)))))))
(fma.f64 (.f64 (pow.f64 z 3) -1/2) (pow.f64 y 5) (fma.f64 (pow.f64 y 3) (pow.f64 z 3) (.f64 (pow.f64 y 7) (fma.f64 (.f64 (.f64 z z) 2/45) z (*.f64 (pow.f64 z 3) 23/360)))))
(fma.f64 (pow.f64 y 5) (.f64 (pow.f64 z 3) -1/2) (fma.f64 (pow.f64 y 3) (pow.f64 z 3) (.f64 (pow.f64 y 7) (fma.f64 (pow.f64 z 3) 23/360 (*.f64 (pow.f64 z 3) 2/45)))))
(fma.f64 (pow.f64 y 7) (.f64 (pow.f64 z 3) 13/120) (.f64 (pow.f64 z 3) (+.f64 (pow.f64 y 3) (*.f64 (pow.f64 y 5) -1/2))))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (pow.f64 z 3)) (.f64 -1/6 (pow.f64 z 3))) (pow.f64 y 5)) (+.f64 (.f64 (pow.f64 y 9) (+.f64 (.f64 -1/6 (.f64 (+.f64 (.f64 1/36 (pow.f64 z 2)) (.f64 1/60 (pow.f64 z 2))) z)) (+.f64 (.f64 z (+.f64 (.f64 -1/360 (pow.f64 z 2)) (.f64 -1/2520 (pow.f64 z 2)))) (+.f64 (.f64 -1/5040 (pow.f64 z 3)) (.f64 -1/360 (pow.f64 z 3)))))) (+.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 z 2)) (.f64 1/60 (pow.f64 z 2))) z) (+.f64 (.f64 1/18 (pow.f64 z 3)) (.f64 1/120 (pow.f64 z 3))))))))
(fma.f64 (.f64 (pow.f64 z 3) -1/2) (pow.f64 y 5) (fma.f64 (pow.f64 y 9) (fma.f64 -1/6 (.f64 z (.f64 (.f64 z z) 2/45)) (fma.f64 z (.f64 (.f64 z z) -1/315) (.f64 (pow.f64 z 3) -1/336))) (fma.f64 (pow.f64 y 3) (pow.f64 z 3) (.f64 (pow.f64 y 7) (fma.f64 (.f64 (.f64 z z) 2/45) z (*.f64 (pow.f64 z 3) 23/360))))))
(fma.f64 (pow.f64 y 5) (.f64 (pow.f64 z 3) -1/2) (fma.f64 (pow.f64 y 9) (fma.f64 -1/6 (.f64 (pow.f64 z 3) 2/45) (fma.f64 (pow.f64 z 3) -1/336 (.f64 (pow.f64 z 3) -1/315))) (fma.f64 (pow.f64 y 3) (pow.f64 z 3) (.f64 (pow.f64 y 7) (fma.f64 (pow.f64 z 3) 23/360 (*.f64 (pow.f64 z 3) 2/45))))))
(fma.f64 (pow.f64 y 9) (+.f64 (.f64 (pow.f64 z 3) -1/135) (.f64 (pow.f64 z 3) -31/5040)) (fma.f64 (pow.f64 y 7) (.f64 (pow.f64 z 3) 13/120) (.f64 (pow.f64 z 3) (+.f64 (pow.f64 y 3) (*.f64 (pow.f64 y 5) -1/2)))))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) x)
(+.f64 x (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) x)
(+.f64 x (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) x)
(+.f64 x (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) x)
(+.f64 x (*.f64 z (sin.f64 y)))
(fma.f64 z (sin.f64 y) x)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y))))
(neg.f64 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 z)))
(.f64 z (.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))))
(+.f64 (.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y)))) x)
(fma.f64 -1 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)) x)
(fma.f64 (neg.f64 (cbrt.f64 -1)) (*.f64 z (sin.f64 y)) x)
(fma.f64 (*.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)) x)
(fma.f64 z (*.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y)))) x)
(fma.f64 -1 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)) x)
(fma.f64 (neg.f64 (cbrt.f64 -1)) (*.f64 z (sin.f64 y)) x)
(fma.f64 (*.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)) x)
(fma.f64 z (*.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 z (sin.f64 y)))) x)
(fma.f64 -1 (.f64 (.f64 z (sin.f64 y)) (cbrt.f64 -1)) x)
(fma.f64 (neg.f64 (cbrt.f64 -1)) (*.f64 z (sin.f64 y)) x)
(fma.f64 (*.f64 z (sin.f64 y)) (neg.f64 (cbrt.f64 -1)) x)
(fma.f64 z (*.f64 (sin.f64 y) (neg.f64 (cbrt.f64 -1))) x)
x
(+.f64 (*.f64 y z) x)
(fma.f64 y z x)
(fma.f64 z y x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (*.f64 (pow.f64 y 3) z)) x))
(fma.f64 y z (fma.f64 -1/6 (*.f64 z (pow.f64 y 3)) x))
(fma.f64 z y (fma.f64 -1/6 (*.f64 z (pow.f64 y 3)) x))
(fma.f64 z (fma.f64 -1/6 (pow.f64 y 3) y) x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 1/120 (*.f64 (pow.f64 y 5) z)) x)))
(fma.f64 y z (fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 1/120 (.f64 z (pow.f64 y 5)) x)))
(fma.f64 z y (fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 1/120 (.f64 z (pow.f64 y 5)) x)))
(fma.f64 z (fma.f64 -1/6 (pow.f64 y 3) y) (fma.f64 1/120 (*.f64 z (pow.f64 y 5)) x))
(fma.f64 z (+.f64 y (fma.f64 -1/6 (pow.f64 y 3) (*.f64 1/120 (pow.f64 y 5)))) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 y)
✓	0.0b	(sqrt.f64 (*.f64 x (cos.f64 y)))
	0.1b	(*.f64 x (cos.f64 y))
✓	0.3b	(pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 2)

Compiler

Compiled 39 to 13 computations (66.7% saved)

series9.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 2)
1.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 2)
1.0ms	y	@	0	(pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 2)
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 2)
1.0ms	y	@	-inf	(pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 2)

rewrite54.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

613×	`pow1_binary64`
565×	`add-log-exp_binary64`
565×	`log1p-expm1-u_binary64`
565×	`expm1-log1p-u_binary64`
551×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	163	14
2	1592	14

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 2)
(sqrt.f64 (*.f64 x (cos.f64 y)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (cos.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (cos.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (cos.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) (sqrt.f64 (*.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))) (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 2) (cbrt.f64 (*.f64 x (cos.f64 y))))))) (#(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 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.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 (sqrt.f64 x) (*.f64 (sqrt.f64 (cos.f64 y)) (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (cos.f64 y)) 1/4) (*.f64 (pow.f64 (*.f64 x (cos.f64 y)) 1/4) (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(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 (*.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) (pow.f64 (*.f64 x (cos.f64 y)) 1/4)) (pow.f64 (*.f64 x (cos.f64 y)) 1/4))))) (#(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 (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 (sqrt.f64 (*.f64 x (cos.f64 y))) (cbrt.f64 (*.f64 x (cos.f64 y)))) (cbrt.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) (sqrt.f64 x)) (sqrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (cos.f64 y))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (cos.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) (cbrt.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))) (cbrt.f64 (*.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (cos.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (cos.f64 y)) 1/4) (pow.f64 (*.f64 x (cos.f64 y)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 y)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cos.f64 y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (cos.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (cos.f64 y)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (cos.f64 y)))))))))

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

428×	`*-commutative_binary64`
397×	`distribute-rgt-in_binary64`
390×	`distribute-lft-in_binary64`
294×	`unswap-sqr_binary64`
275×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	353
1	148	349
2	412	298
3	1786	277
4	5247	277

Stop Event

1×	node limit

Counts

74 → 66

Calls

Call 1

Inputs
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/24 x) (.f64 1/16 x)) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2))) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/24 x) (.f64 1/16 x)) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 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)
(sqrt.f64 x)
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 x))) (sqrt.f64 x))
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 x))) (+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (pow.f64 (*.f64 -1/4 (sqrt.f64 x)) 2))) (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)))
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 x))) (+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2))) (sqrt.f64 (/.f64 1 x)))) (+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 (.f64 (pow.f64 y 6) (-.f64 (.f64 -1/720 x) (.f64 -1/4 (-.f64 (.f64 1/24 x) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2))))) (sqrt.f64 (/.f64 1 x)))))))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 (cos.f64 y) x))

Outputs
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(.f64 x (fma.f64 -1/2 (.f64 y y) 1))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/24 x) (.f64 1/16 x)) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2))) x))
(fma.f64 -1/2 (.f64 x (.f64 y y)) (fma.f64 (pow.f64 y 4) (-.f64 (.f64 x 5/48) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2)) x))
(fma.f64 x (.f64 -1/2 (.f64 y y)) (fma.f64 (pow.f64 y 4) (fma.f64 x 5/48 (*.f64 x -1/16)) x))
(.f64 x (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (*.f64 (pow.f64 y 4) 1/24)))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/24 x) (.f64 1/16 x)) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2))) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 -1/2 (.f64 x (.f64 y y)) (fma.f64 (pow.f64 y 4) (-.f64 (.f64 x 5/48) (pow.f64 (*.f64 -1/4 (sqrt.f64 x)) 2)) x)))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 -1/2 (.f64 y y))) (fma.f64 (pow.f64 y 4) (fma.f64 x 5/48 (*.f64 x -1/16)) x))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 -1/2 (.f64 y y))) (fma.f64 (pow.f64 y 4) (*.f64 x 1/24) x))
(*.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))
(sqrt.f64 x)
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 x))) (sqrt.f64 x))
(fma.f64 -1/4 (.f64 (.f64 y y) (sqrt.f64 x)) (sqrt.f64 x))
(fma.f64 -1/4 (.f64 y (.f64 y (sqrt.f64 x))) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (fma.f64 (.f64 y y) -1/4 1))
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 x))) (+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (pow.f64 (*.f64 -1/4 (sqrt.f64 x)) 2))) (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)))
(fma.f64 -1/4 (.f64 (.f64 y y) (sqrt.f64 x)) (fma.f64 1/2 (.f64 (pow.f64 y 4) (.f64 (-.f64 (.f64 x 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)))
(fma.f64 -1/4 (.f64 y (.f64 y (sqrt.f64 x))) (fma.f64 1/2 (.f64 (pow.f64 y 4) (.f64 (-.f64 (.f64 x 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)))
(fma.f64 (pow.f64 y 4) (.f64 1/2 (.f64 (fma.f64 x 1/24 (.f64 x -1/16)) (sqrt.f64 (/.f64 1 x)))) (.f64 (sqrt.f64 x) (fma.f64 (*.f64 y y) -1/4 1)))
(fma.f64 (fma.f64 (.f64 y y) -1/4 1) (sqrt.f64 x) (.f64 (pow.f64 y 4) (.f64 1/2 (.f64 (*.f64 x -1/48) (sqrt.f64 (/.f64 1 x))))))
(fma.f64 (fma.f64 (.f64 y y) -1/4 1) (sqrt.f64 x) (.f64 (pow.f64 y 4) (.f64 (sqrt.f64 (/.f64 1 x)) (.f64 1/2 (*.f64 x -1/48)))))
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 x))) (+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 x) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2))) (sqrt.f64 (/.f64 1 x)))) (+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 (.f64 (pow.f64 y 6) (-.f64 (.f64 -1/720 x) (.f64 -1/4 (-.f64 (.f64 1/24 x) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2))))) (sqrt.f64 (/.f64 1 x)))))))
(fma.f64 -1/4 (.f64 (.f64 y y) (sqrt.f64 x)) (+.f64 (fma.f64 1/2 (.f64 (pow.f64 y 4) (.f64 (-.f64 (.f64 x 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 x)) (.f64 (pow.f64 y 6) (-.f64 (.f64 x -1/720) (.f64 -1/4 (-.f64 (.f64 x 1/24) (pow.f64 (*.f64 -1/4 (sqrt.f64 x)) 2)))))))))
(fma.f64 -1/4 (.f64 y (.f64 y (sqrt.f64 x))) (fma.f64 1/2 (.f64 (pow.f64 y 4) (.f64 (-.f64 (.f64 x 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (fma.f64 1/2 (.f64 (fma.f64 x -1/720 (.f64 (-.f64 (.f64 x 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 x)) 2)) 1/4)) (*.f64 (pow.f64 y 6) (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))))
(+.f64 (.f64 (sqrt.f64 x) (fma.f64 (.f64 y y) -1/4 1)) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 (pow.f64 y 4) (fma.f64 x 1/24 (.f64 x -1/16))) (.f64 (pow.f64 y 6) (fma.f64 (fma.f64 x 1/24 (.f64 x -1/16)) 1/4 (*.f64 x -1/720))))))
(+.f64 (.f64 (sqrt.f64 x) (fma.f64 (.f64 y y) -1/4 1)) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 (pow.f64 y 4) (.f64 x -1/48)) (.f64 (pow.f64 y 6) (fma.f64 x -1/720 (.f64 -1/4 (*.f64 x 1/48)))))))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))
(sqrt.f64 (*.f64 (cos.f64 y) x))
(sqrt.f64 (*.f64 x (cos.f64 y)))

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.3b	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
✓	0.3b	(pow.f64 (cos.f64 y) 3)
✓	39.8b	(cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3)))

Compiler

Compiled 53 to 29 computations (45.3% saved)

series15.0ms (0.1%)

Counts

3 → 32

Calls

15 calls:

Time	Variable		Point	Expression
7.0ms	y	@	inf	(pow.f64 (cos.f64 y) 3)
1.0ms	x	@	0	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
1.0ms	y	@	inf	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
1.0ms	y	@	-inf	(pow.f64 (cos.f64 y) 3)
1.0ms	y	@	0	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))

rewrite75.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`pow1_binary64`
722×	`add-log-exp_binary64`
722×	`log1p-expm1-u_binary64`
722×	`expm1-log1p-u_binary64`
700×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	194	21
2	2045	21

Stop Event

1×	node limit

Counts

3 → 56

Calls

Call 1

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

Outputs

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

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

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

simplify112.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1334×	`unswap-sqr_binary64`
629×	`distribute-lft-out_binary64`
428×	`*-commutative_binary64`
348×	`fma-neg_binary64`
345×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	360
1	141	344
2	449	324
3	1773	318
4	3295	318
5	3904	318
6	4490	318
7	4748	318
8	5036	318
9	5944	318

Stop Event

1×	node limit

Counts

88 → 79

Calls

Call 1

Inputs
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) 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)
(*.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)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
1
(+.f64 1 (*.f64 -3/2 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 7/8 (pow.f64 y 4)) (.f64 -3/2 (pow.f64 y 2))))
(+.f64 1 (+.f64 (.f64 -61/240 (pow.f64 y 6)) (+.f64 (.f64 7/8 (pow.f64 y 4)) (*.f64 -3/2 (pow.f64 y 2)))))
(pow.f64 x 3)
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 x 3))) (pow.f64 x 3))
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (pow.f64 x 3)))
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (pow.f64 x 3) (.f64 -61/240 (.f64 (pow.f64 y 6) (pow.f64 x 3))))))

Outputs
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(fma.f64 x (.f64 -1/2 (.f64 y y)) x)
(.f64 x (fma.f64 (.f64 -1/2 y) y 1))
(.f64 x (fma.f64 -1/2 (.f64 y y) 1))
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(fma.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 -1/2 (.f64 y y))) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 1/24 (pow.f64 y 4))) (fma.f64 x (.f64 -1/2 (*.f64 y y)) x))
(.f64 x (+.f64 (fma.f64 (.f64 -1/2 y) y 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(.f64 x (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(*.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))
(*.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))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 x (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 x (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 x (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 x (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
1
(+.f64 1 (*.f64 -3/2 (pow.f64 y 2)))
(+.f64 1 (.f64 (.f64 y y) -3/2))
(fma.f64 (*.f64 y y) -3/2 1)
(fma.f64 y (*.f64 y -3/2) 1)
(+.f64 1 (+.f64 (.f64 7/8 (pow.f64 y 4)) (.f64 -3/2 (pow.f64 y 2))))
(+.f64 1 (fma.f64 7/8 (pow.f64 y 4) (.f64 (.f64 y y) -3/2)))
(+.f64 (fma.f64 (.f64 y y) -3/2 1) (.f64 (pow.f64 y 4) 7/8))
(fma.f64 (pow.f64 y 4) 7/8 (fma.f64 (*.f64 y y) -3/2 1))
(fma.f64 y (*.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1))
(+.f64 1 (+.f64 (.f64 -61/240 (pow.f64 y 6)) (+.f64 (.f64 7/8 (pow.f64 y 4)) (*.f64 -3/2 (pow.f64 y 2)))))
(+.f64 1 (fma.f64 -61/240 (pow.f64 y 6) (fma.f64 7/8 (pow.f64 y 4) (.f64 (.f64 y y) -3/2))))
(+.f64 1 (fma.f64 (pow.f64 y 6) -61/240 (fma.f64 (.f64 y y) -3/2 (.f64 (pow.f64 y 4) 7/8))))
(fma.f64 (pow.f64 y 6) -61/240 (fma.f64 (pow.f64 y 4) 7/8 (fma.f64 (*.f64 y y) -3/2 1)))
(fma.f64 (pow.f64 y 6) -61/240 (fma.f64 y (*.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1)))
(pow.f64 x 3)
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 x 3))) (pow.f64 x 3))
(fma.f64 -3/2 (.f64 (.f64 y y) (pow.f64 x 3)) (pow.f64 x 3))
(.f64 (fma.f64 (.f64 y y) -3/2 1) (pow.f64 x 3))
(.f64 (fma.f64 y (.f64 y -3/2) 1) (pow.f64 x 3))
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (pow.f64 x 3)))
(fma.f64 -3/2 (.f64 (.f64 y y) (pow.f64 x 3)) (fma.f64 7/8 (*.f64 (pow.f64 y 4) (pow.f64 x 3)) (pow.f64 x 3)))
(+.f64 (pow.f64 x 3) (.f64 (pow.f64 x 3) (fma.f64 (.f64 y y) -3/2 (*.f64 (pow.f64 y 4) 7/8))))
(.f64 (pow.f64 x 3) (fma.f64 (pow.f64 y 4) 7/8 (fma.f64 (.f64 y y) -3/2 1)))
(.f64 (fma.f64 (pow.f64 y 4) 7/8 (fma.f64 (.f64 y y) -3/2 1)) (pow.f64 x 3))
(.f64 (fma.f64 y (.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1)) (pow.f64 x 3))
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 x 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (pow.f64 x 3) (.f64 -61/240 (.f64 (pow.f64 y 6) (pow.f64 x 3))))))
(fma.f64 -3/2 (.f64 (.f64 y y) (pow.f64 x 3)) (fma.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (+.f64 (pow.f64 x 3) (.f64 -61/240 (*.f64 (pow.f64 y 6) (pow.f64 x 3))))))
(+.f64 (.f64 (+.f64 1 (.f64 (pow.f64 y 6) -61/240)) (pow.f64 x 3)) (.f64 (pow.f64 x 3) (fma.f64 (.f64 y y) -3/2 (*.f64 (pow.f64 y 4) 7/8))))
(+.f64 (pow.f64 x 3) (.f64 (pow.f64 x 3) (fma.f64 y (.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 (*.f64 (pow.f64 y 6) -61/240)))))
(.f64 (pow.f64 x 3) (fma.f64 (pow.f64 y 6) -61/240 (fma.f64 (pow.f64 y 4) 7/8 (fma.f64 (.f64 y y) -3/2 1))))
(.f64 (fma.f64 (pow.f64 y 6) -61/240 (fma.f64 (pow.f64 y 4) 7/8 (fma.f64 (.f64 y y) -3/2 1))) (pow.f64 x 3))
(.f64 (fma.f64 (pow.f64 y 6) -61/240 (fma.f64 y (.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1))) (pow.f64 x 3))

eval170.0ms (1.7%)

Compiler: Compiled 9820 to 4818 computations (50.9% saved)

prune131.0ms (1.3%)

Pruning

23 alts after pruning (14 fresh and 9 done)

	Pruned	Kept	Total
New	602	7	609
Fresh	2	7	9
Picked	1	0	1
Done	4	9	13
Total	609	23	632

Error

0.0b

Counts

632 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	2.9b	(fma.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) z) (.f64 x (cos.f64 y)))
	0.2b	(+.f64 (.f64 x (+.f64 (+.f64 (cos.f64 y) -1) 1)) (.f64 z (sin.f64 y)))
	24.1b	(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 y z))
✓	0.9b	(+.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
	54.1b	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
	24.1b	(+.f64 (.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1)) (.f64 y z))
✓	42.5b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 y z))
	0.6b	(fma.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (.f64 x (cos.f64 y)))
✓	31.2b	(+.f64 (*.f64 y z) x)
✓	0.2b	(+.f64 (.f64 x (log1p.f64 (expm1.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
	24.2b	(*.f64 (cos.f64 y) x)
	37.3b	(+.f64 x (.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
	40.0b	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
	31.2b	(fma.f64 z y x)
	0.5b	(+.f64 (+.f64 (.f64 (+.f64 1 (cos.f64 y)) x) (.f64 -1 x)) (*.f64 z (sin.f64 y)))
✓	15.7b	(+.f64 x (*.f64 z (sin.f64 y)))
	0.3b	(+.f64 (+.f64 x (.f64 (+.f64 (cos.f64 y) -1) x)) (.f64 z (sin.f64 y)))
✓	54.5b	(*.f64 y z)
✓	39.7b	(*.f64 z (sin.f64 y))
	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
	38.5b	x
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))

Compiler

Compiled 275 to 192 computations (30.2% saved)

regimes114.0ms (1.1%)

Counts

47 → 1

Calls

Call 1

Inputs
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))
(fma.f64 z y x)
(fma.f64 z y x)
(*.f64 z (sin.f64 y))
(*.f64 (cos.f64 y) x)
(fma.f64 y z x)
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
(+.f64 (.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1)) (.f64 y z))
(+.f64 (.f64 y z) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (+.f64 (+.f64 (cos.f64 y) -1) 1)) (.f64 z (sin.f64 y)))
(+.f64 (+.f64 x (.f64 (+.f64 (cos.f64 y) -1) x)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1)) (.f64 z (sin.f64 y)))
(+.f64 (+.f64 (.f64 (+.f64 1 (cos.f64 y)) x) (.f64 -1 x)) (*.f64 z (sin.f64 y)))
(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))
(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
(+.f64 x (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
(+.f64 x (.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 y z))
(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 y z))
(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 y z))
(+.f64 (.f64 x (pow.f64 (sqrt.f64 (cos.f64 y)) 2)) (.f64 y z))
(fma.f64 (*.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) x)
(+.f64 (.f64 x (log1p.f64 (expm1.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (log.f64 (exp.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (pow.f64 (sqrt.f64 (cos.f64 y)) 2)) (.f64 z (sin.f64 y)))
(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
(+.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
(+.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 x (-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1)) (.f64 z (sin.f64 y)))
(fma.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z) (.f64 x (cos.f64 y)))
(+.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))) (.f64 z (sin.f64 y)))
(fma.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (.f64 x (cos.f64 y)))
(fma.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (.f64 (cbrt.f64 (sin.f64 y)) z) (.f64 x (cos.f64 y)))
(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 z (sin.f64 y)))

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

Calls

4 calls:

27.0ms	z
26.0ms	x
25.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
23.0ms	y

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`z`
0.1b	1	`(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))`

Compiler

Compiled 464 to 163 computations (64.9% saved)

regimes82.0ms (0.8%)

Counts

23 → 1

Calls

Call 1

Inputs
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))
(fma.f64 z y x)
(fma.f64 z y x)
(*.f64 z (sin.f64 y))
(*.f64 (cos.f64 y) x)
(fma.f64 y z x)
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
(+.f64 (.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1)) (.f64 y z))
(+.f64 (.f64 y z) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (+.f64 (+.f64 (cos.f64 y) -1) 1)) (.f64 z (sin.f64 y)))
(+.f64 (+.f64 x (.f64 (+.f64 (cos.f64 y) -1) x)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1)) (.f64 z (sin.f64 y)))
(+.f64 (+.f64 (.f64 (+.f64 1 (cos.f64 y)) x) (.f64 -1 x)) (*.f64 z (sin.f64 y)))
(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)

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

Calls

4 calls:

31.0ms	z
17.0ms	y
14.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
12.0ms	x

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`z`
0.1b	1	`(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))`

Compiler

Compiled 187 to 75 computations (59.9% saved)

regimes118.0ms (1.2%)

Counts

16 → 3

Calls

Call 1

Inputs
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))
(fma.f64 z y x)
(fma.f64 z y x)
(*.f64 z (sin.f64 y))
(*.f64 (cos.f64 y) x)
(fma.f64 y z x)
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
(+.f64 (.f64 x (-.f64 (+.f64 1 (cos.f64 y)) 1)) (.f64 y z))
(+.f64 (.f64 y z) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) x)) x))

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

Calls

3 calls:

44.0ms	z
39.0ms	y
32.0ms	x

Results

Error	Segments	Branch
9.1b	3	`x`
11.5b	5	`y`
8.6b	3	`z`

Compiler

Compiled 98 to 36 computations (63.3% saved)

bsearch129.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
65.0ms	7.590471303384688e-28	5.754616414316947e-24
63.0ms	-9.627504454213342e-48	-1.6037779352786074e-56

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes140.0ms (1.4%)

Counts

11 → 6

Calls

Call 1

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

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

Calls

3 calls:

62.0ms	z
39.0ms	y
36.0ms	x

Results

Error	Segments	Branch
16.6b	5	`x`
12.3b	6	`y`
12.8b	7	`z`

Compiler

Compiled 53 to 20 computations (62.3% saved)

bsearch264.0ms (2.7%)

Algorithm

5×	binary-search

Steps

Time	Left	Right
107.0ms	1.1302365386005706e+292	1.8557516269835282e+294
46.0ms	4.6130015529212706e+22	2.793867490671501e+26
37.0ms	3707.5009248211663	50968.686394507786
36.0ms	-560.315978532113	-1.2138740605037355e-11
36.0ms	-7.108449941537077e+56	-2.83703261614331e+46

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes83.0ms (0.8%)

Counts

8 → 3

Calls

Call 1

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

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

Calls

3 calls:

43.0ms	x
22.0ms	z
16.0ms	y

Results

Error	Segments	Branch
27.2b	5	`x`
17.1b	3	`y`
24.8b	3	`z`

Compiler

Compiled 41 to 17 computations (58.5% saved)

bsearch141.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
77.0ms	3707.5009248211663	50968.686394507786
64.0ms	-3156118704422.5156	-4624185.292118354

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes123.0ms (1.2%)

Counts

5 → 3

Calls

Call 1

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

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

Calls

3 calls:

54.0ms	x
36.0ms	z
31.0ms	y

Results

Error	Segments	Branch
27.2b	5	`x`
17.1b	3	`y`
24.8b	3	`z`

Compiler

Compiled 29 to 16 computations (44.8% saved)

bsearch283.0ms (2.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
211.0ms	3707.5009248211663	50968.686394507786
72.0ms	-3156118704422.5156	-4624185.292118354

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes30.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

Inputs
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)

Outputs
(+.f64 (*.f64 y z) x)

Calls

3 calls:

10.0ms	z
9.0ms	x
9.0ms	y

Results

Error	Segments	Branch
31.2b	1	`x`
31.2b	1	`y`
31.2b	1	`z`

Compiler

Compiled 25 to 14 computations (44% saved)

regimes191.0ms (1.9%)

Counts

3 → 5

Calls

Call 1

Inputs
x
x
(*.f64 y z)

Outputs
(*.f64 y z)
x
(*.f64 y z)
x
(*.f64 y z)

Calls

3 calls:

144.0ms	x
37.0ms	z
8.0ms	y

Results

Error	Segments	Branch
37.2b	3	`x`
38.5b	1	`y`
34.8b	5	`z`

Compiler

Compiled 20 to 13 computations (35% saved)

bsearch541.0ms (5.4%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
73.0ms	1.5296243285835838e+247	7.253874911360501e+251
200.0ms	6.65379137851322e+95	1.5054505231053653e+99
123.0ms	9.887965403097091e+48	5.897128711264766e+55
145.0ms	-1.0709395419186857e+182	-4.3558872437979956e+178

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes12.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
x

Outputs
x

Calls

3 calls:

4.0ms	x
3.0ms	y
3.0ms	z

Results

Error	Segments	Branch
38.5b	1	`x`
38.5b	1	`y`
38.5b	1	`z`

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	233
1	62	233

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(if (<=.f64 z -1980262806879783/205688069665150755269371147819668813122841983204197482918576128) (+.f64 x (.f64 z (sin.f64 y))) (if (<=.f64 z 2115914580919257/2787593149816327892691964784081045188247552) (.f64 (cos.f64 y) x) (+.f64 x (*.f64 z (sin.f64 y)))))
(if (<=.f64 y -710844994153707735647811980643986380147429227953131618304) (.f64 z (sin.f64 y)) (if (<=.f64 y -4928591468997967/8796093022208) (.f64 (cos.f64 y) x) (if (<=.f64 y 2038220188415573/549755813888) (fma.f64 z y x) (if (<=.f64 y 46130015529212705767424) (.f64 z (sin.f64 y)) (if (<=.f64 y 11302365386005705969829860357121101009451148854983543498752484176718583297252056723824150291489335622641364144222818291126723754678282039725677117437532060318217757277484807578658303239880541734416533107456648593096138269449843783096603844758977058045263024402301940070419644721776007434993664) (.f64 (cos.f64 y) x) (*.f64 z (sin.f64 y)))))))
(if (<=.f64 y -201991597083041/64) (.f64 z (sin.f64 y)) (if (<=.f64 y 2038220188415573/549755813888) (fma.f64 z y x) (.f64 z (sin.f64 y))))
(if (<=.f64 y -201991597083041/64) (.f64 z (sin.f64 y)) (if (<=.f64 y 2038220188415573/549755813888) (+.f64 (.f64 y z) x) (*.f64 z (sin.f64 y))))
(+.f64 (*.f64 y z) x)
(if (<=.f64 z -107093954191868566954712351631271911165464031735763090106569004260916044025524024176890575656856641401285214386162701926484978027083583972339573357993284339065702985268454226558713856) (.f64 y z) (if (<=.f64 z 9887965403097090940782268240236306957089581826048) x (if (<=.f64 z 665379137851321945694208156143063844655933132780705798268289399623013380105429957721072122986496) (.f64 y z) (if (<=.f64 z 15296243285835838089036886032937015360081233924950705150560697611089319745343446777674401045460125604010515191844020925100047909550831532854255205951215801803464067243149021070165346203841424389670199817765858904755505503137942067760755345459249152) x (*.f64 y z)))))
x

Outputs
(fma.f64 (sin.f64 y) z (*.f64 x (cos.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (sin.f64 y) z) (.f64 x (cos.f64 y)))
(if (<=.f64 z -1980262806879783/205688069665150755269371147819668813122841983204197482918576128) (+.f64 x (.f64 z (sin.f64 y))) (if (<=.f64 z 2115914580919257/2787593149816327892691964784081045188247552) (.f64 (cos.f64 y) x) (+.f64 x (*.f64 z (sin.f64 y)))))
(if (<=.f64 z -1980262806879783/205688069665150755269371147819668813122841983204197482918576128) (+.f64 x (.f64 (sin.f64 y) z)) (if (<=.f64 z 2115914580919257/2787593149816327892691964784081045188247552) (.f64 x (cos.f64 y)) (+.f64 x (*.f64 (sin.f64 y) z))))
(if (<=.f64 y -710844994153707735647811980643986380147429227953131618304) (.f64 z (sin.f64 y)) (if (<=.f64 y -4928591468997967/8796093022208) (.f64 (cos.f64 y) x) (if (<=.f64 y 2038220188415573/549755813888) (fma.f64 z y x) (if (<=.f64 y 46130015529212705767424) (.f64 z (sin.f64 y)) (if (<=.f64 y 11302365386005705969829860357121101009451148854983543498752484176718583297252056723824150291489335622641364144222818291126723754678282039725677117437532060318217757277484807578658303239880541734416533107456648593096138269449843783096603844758977058045263024402301940070419644721776007434993664) (.f64 (cos.f64 y) x) (*.f64 z (sin.f64 y)))))))
(if (<=.f64 y -710844994153707735647811980643986380147429227953131618304) (.f64 (sin.f64 y) z) (if (<=.f64 y -4928591468997967/8796093022208) (.f64 x (cos.f64 y)) (if (<=.f64 y 2038220188415573/549755813888) (fma.f64 z y x) (if (<=.f64 y 46130015529212705767424) (.f64 (sin.f64 y) z) (if (<=.f64 y 11302365386005705969829860357121101009451148854983543498752484176718583297252056723824150291489335622641364144222818291126723754678282039725677117437532060318217757277484807578658303239880541734416533107456648593096138269449843783096603844758977058045263024402301940070419644721776007434993664) (.f64 x (cos.f64 y)) (*.f64 (sin.f64 y) z))))))
(if (<=.f64 y -201991597083041/64) (.f64 z (sin.f64 y)) (if (<=.f64 y 2038220188415573/549755813888) (fma.f64 z y x) (.f64 z (sin.f64 y))))
(if (<=.f64 y -201991597083041/64) (.f64 (sin.f64 y) z) (if (<=.f64 y 2038220188415573/549755813888) (fma.f64 z y x) (.f64 (sin.f64 y) z)))
(if (<=.f64 y -201991597083041/64) (.f64 z (sin.f64 y)) (if (<=.f64 y 2038220188415573/549755813888) (+.f64 (.f64 y z) x) (*.f64 z (sin.f64 y))))
(if (<=.f64 y -201991597083041/64) (.f64 (sin.f64 y) z) (if (<=.f64 y 2038220188415573/549755813888) (+.f64 x (.f64 y z)) (*.f64 (sin.f64 y) z)))
(+.f64 (*.f64 y z) x)
(+.f64 x (*.f64 y z))
(if (<=.f64 z -107093954191868566954712351631271911165464031735763090106569004260916044025524024176890575656856641401285214386162701926484978027083583972339573357993284339065702985268454226558713856) (.f64 y z) (if (<=.f64 z 9887965403097090940782268240236306957089581826048) x (if (<=.f64 z 665379137851321945694208156143063844655933132780705798268289399623013380105429957721072122986496) (.f64 y z) (if (<=.f64 z 15296243285835838089036886032937015360081233924950705150560697611089319745343446777674401045460125604010515191844020925100047909550831532854255205951215801803464067243149021070165346203841424389670199817765858904755505503137942067760755345459249152) x (*.f64 y z)))))
x

Compiler

Compiled 186 to 101 computations (45.7% saved)

soundness0.0ms (0%)

end218.0ms (2.2%)

Compiler: Compiled 162 to 58 computations (64.2% saved)