Details

analyze528.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (40.1%)

Results

1.5s	2035×	body	1024	valid
1.1s	5163×	body	256	valid
593.0ms	1050×	body	512	valid
8.0ms	8×	body	2048	valid

preprocess25.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

10×	`*-commutative_binary64`
9×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	20	22
2	31	22
3	44	22
4	52	22
5	61	22
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))

Outputs
(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))
(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
(.f64 (/.f64 8/3 (sin.f64 x)) (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
9×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	20	22
2	31	22
3	44	22
4	52	22
5	61	22

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))

Outputs
(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))
(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
(.f64 (/.f64 8/3 (sin.f64 x)) (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))

eval2.0ms (0%)

Compiler: Compiled 31 to 24 computations (22.6% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

11.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	11.1b	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
▶	11.2b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))
✓	0.4b	(/.f64 8/3 (sin.f64 x))
✓	11.0b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 40 to 28 computations (30% saved)

series12.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))
2.0ms	x	@	-inf	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))
2.0ms	x	@	0	(.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))
2.0ms	x	@	inf	(/.f64 8/3 (sin.f64 x))
1.0ms	x	@	0	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))

rewrite118.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`prod-diff_binary64`
500×	`log-prod_binary64`
283×	`pow-prod-down_binary64`
271×	`pow2_binary64`
190×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	220	32
2	2873	32

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))
(/.f64 8/3 (sin.f64 x))
(.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (.f64 (sin.f64 x) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (cos.f64 x)) 1) (.f64 2 (.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (cos.f64 x)) -8/3) (.f64 2 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 8/3 (-.f64 1 (cos.f64 x))) (.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -8/3 (-.f64 1 (cos.f64 x))) (.f64 (neg.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3) 1) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3) (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -8/3 (+.f64 1/2 (.f64 -1/2 (cos.f64 x)))) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) -8/3) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x))))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 8/3 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 8/3 (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 8/3 (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 8/3 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 8/3 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 8/3 (sin.f64 x))) (cbrt.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 8/3 (sin.f64 x))) (sqrt.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -8/3 (/.f64 1 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sin.f64 x)) 8/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 8/3 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 8/3 (sin.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 8/3 (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sin.f64 x) 3/8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (sin.f64 x) 3/8) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 8/3 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 8/3 (sin.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 8/3 (sin.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (sin.f64 x) 3/8)) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (neg.f64 (.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (.f64 -1/2 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (.f64 1/2 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (/.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (pow.f64 (.f64 1/2 (cos.f64 x)) 3)) (+.f64 1/4 (+.f64 (pow.f64 (.f64 1/2 (cos.f64 x)) 2) (.f64 1/2 (.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (.f64 1/2 (cos.f64 x)) 2)) (/.f64 (+.f64 (cos.f64 x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (sin.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sin.f64 (.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (sin.f64 (.f64 x 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))))) 3))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (*.f64 (sin.f64 x) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sin.f64 x) (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) 3/8) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 8/3) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 8/3)) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (*.f64 2 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) 1) (*.f64 2 (*.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) -8/3) (*.f64 2 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 8/3 (-.f64 1 (cos.f64 x))) (*.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -8/3 (-.f64 1 (cos.f64 x))) (*.f64 (neg.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 8/3) 1) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 8/3) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 8/3) (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -8/3 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x)))) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) -8/3) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 8/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x))))) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 8/3 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 8/3 (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8/3 (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8/3 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 8/3 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 8/3 (sin.f64 x))) (cbrt.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 8/3 (sin.f64 x))) (sqrt.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -8/3 (/.f64 1 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sin.f64 x)) 8/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 8/3 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 8/3 (sin.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 8/3 (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sin.f64 x) 3/8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 8/3 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 8/3 (sin.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 8/3 (sin.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) 3/8)) -1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (neg.f64 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 -1/2 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (/.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (pow.f64 (*.f64 1/2 (cos.f64 x)) 3)) (+.f64 1/4 (+.f64 (pow.f64 (*.f64 1/2 (cos.f64 x)) 2) (*.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (*.f64 1/2 (cos.f64 x)) 2)) (/.f64 (+.f64 (cos.f64 x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))))) 3))))))

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-def_binary64`
753×	`distribute-lft-out_binary64`
711×	`distribute-rgt-out_binary64`
696×	`associate-l_binary64`
556×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	385
1	154	385
2	365	385
3	1092	385
4	4364	385
5	6930	385

Stop Event

1×	node limit

Counts

130 → 127

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 8/3 x)
(+.f64 (.f64 4/9 x) (.f64 8/3 (/.f64 1 x)))
(+.f64 (.f64 4/9 x) (+.f64 (.f64 7/135 (pow.f64 x 3)) (*.f64 8/3 (/.f64 1 x))))
(+.f64 (.f64 4/9 x) (+.f64 (.f64 31/5670 (pow.f64 x 5)) (+.f64 (.f64 7/135 (pow.f64 x 3)) (.f64 8/3 (/.f64 1 x)))))
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 3))))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 2/3 x))))
(fma.f64 x (fma.f64 1/18 (.f64 x x) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (.f64 x (fma.f64 1/18 (.f64 x x) 2/3))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 x)
(+.f64 (.f64 4/9 x) (.f64 8/3 (/.f64 1 x)))
(fma.f64 4/9 x (/.f64 8/3 x))
(fma.f64 x 4/9 (/.f64 8/3 x))
(+.f64 (.f64 4/9 x) (+.f64 (.f64 7/135 (pow.f64 x 3)) (*.f64 8/3 (/.f64 1 x))))
(fma.f64 4/9 x (fma.f64 7/135 (pow.f64 x 3) (/.f64 8/3 x)))
(fma.f64 x 4/9 (fma.f64 (pow.f64 x 3) 7/135 (/.f64 8/3 x)))
(fma.f64 x (fma.f64 x (*.f64 x 7/135) 4/9) (/.f64 8/3 x))
(+.f64 (.f64 4/9 x) (+.f64 (.f64 31/5670 (pow.f64 x 5)) (+.f64 (.f64 7/135 (pow.f64 x 3)) (.f64 8/3 (/.f64 1 x)))))
(fma.f64 4/9 x (fma.f64 31/5670 (pow.f64 x 5) (fma.f64 7/135 (pow.f64 x 3) (/.f64 8/3 x))))
(fma.f64 x 4/9 (fma.f64 (pow.f64 x 5) 31/5670 (fma.f64 (pow.f64 x 3) 7/135 (/.f64 8/3 x))))
(fma.f64 x 4/9 (fma.f64 31/5670 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) 7/135 (/.f64 8/3 x))))
(fma.f64 x (fma.f64 x (*.f64 x 7/135) 4/9) (fma.f64 31/5670 (pow.f64 x 5) (/.f64 8/3 x)))
(*.f64 1/4 (pow.f64 x 2))
(.f64 1/4 (.f64 x x))
(.f64 x (.f64 x 1/4))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 1/4 (.f64 x x) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 x (.f64 x 1/4) (.f64 -1/48 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/48) 1/4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/48) 1/4))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 x (.f64 x 1/4) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/48) 1/4) (*.f64 1/1440 (pow.f64 x 6)))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 x (.f64 x 1/4) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 x (.f64 x 1/4) (fma.f64 1/1440 (pow.f64 x 6) (fma.f64 -1/48 (pow.f64 x 4) (.f64 -1/80640 (pow.f64 x 8)))))
(fma.f64 -1/48 (pow.f64 x 4) (fma.f64 1/1440 (pow.f64 x 6) (fma.f64 -1/80640 (pow.f64 x 8) (.f64 x (.f64 x 1/4)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)

localize32.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))
✓	0.3b	(.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2)))
✓	10.9b	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))

New

Error

Program

✓

0.3b

(*.f64 (*.f64 (/.f64 8 3) (sin.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))

✓

0.3b

(*.f64 (/.f64 8 3) (sin.f64 (*.f64 x 1/2)))

✓

10.9b

(/.f64 (*.f64 (*.f64 (/.f64 8 3) (sin.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2))) (sin.f64 x))

Compiler

Compiled 54 to 43 computations (20.4% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	-inf	(.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	inf	(.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	-inf	(.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	0	(.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2)))

rewrite83.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`log-prod_binary64`
452×	`exp-prod_binary64`
305×	`pow2_binary64`
296×	`pow-prod-down_binary64`
215×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	251	38
2	2994	38

Stop Event

1×	node limit

Counts

3 → 109

Calls

Call 1

Inputs

(/.f64 (*.f64 (*.f64 (/.f64 8 3) (sin.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2))) (sin.f64 x))

(*.f64 (/.f64 8 3) (sin.f64 (*.f64 x 1/2)))

(*.f64 (*.f64 (/.f64 8 3) (sin.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 8/3 (.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 64/9 (pow.f64 (sin.f64 (.f64 x 1/2)) 4))) (.f64 (cbrt.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x)))))) (cbrt.f64 (pow.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) 2)) (cbrt.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (/.f64 1 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sin.f64 (.f64 x 1/2)) 1) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) 1) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 64/9 (pow.f64 (sin.f64 (.f64 x 1/2)) 4))) 1) (/.f64 (cbrt.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 1) (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 8/3 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sin.f64 (.f64 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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 64/9 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 2)) (cbrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (sqrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 64/9 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1) 1))))))

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
783×	`distribute-rgt-out_binary64`
772×	`distribute-lft-out_binary64`
688×	`associate-l_binary64`
554×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	490
1	157	490
2	374	490
3	1111	490
4	4229	490
5	6972	490

Stop Event

1×	node limit

Counts

145 → 138

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(*.f64 4/3 x)
(+.f64 (.f64 4/3 x) (.f64 -1/18 (pow.f64 x 3)))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (*.f64 -1/18 (pow.f64 x 3))))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 -1/241920 (pow.f64 x 7)) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (.f64 -1/18 (pow.f64 x 3)))))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(*.f64 2/3 (pow.f64 x 2))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (.f64 2/3 (pow.f64 x 2)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (*.f64 1/540 (pow.f64 x 6))))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (+.f64 (.f64 -1/30240 (pow.f64 x 8)) (.f64 1/540 (pow.f64 x 6)))))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 3))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (.f64 1/180 (pow.f64 x 5)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 2/3 x (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(*.f64 4/3 x)
(*.f64 x 4/3)
(+.f64 (.f64 4/3 x) (.f64 -1/18 (pow.f64 x 3)))
(fma.f64 4/3 x (*.f64 (pow.f64 x 3) -1/18))
(fma.f64 (pow.f64 x 3) -1/18 (*.f64 x 4/3))
(fma.f64 x 4/3 (*.f64 (pow.f64 x 3) -1/18))
(.f64 x (fma.f64 x (.f64 x -1/18) 4/3))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (*.f64 -1/18 (pow.f64 x 3))))
(fma.f64 4/3 x (fma.f64 1/1440 (pow.f64 x 5) (*.f64 (pow.f64 x 3) -1/18)))
(fma.f64 x 4/3 (fma.f64 (pow.f64 x 3) -1/18 (*.f64 (pow.f64 x 5) 1/1440)))
(fma.f64 x (fma.f64 x (.f64 x -1/18) 4/3) (.f64 (pow.f64 x 5) 1/1440))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 -1/241920 (pow.f64 x 7)) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (.f64 -1/18 (pow.f64 x 3)))))
(fma.f64 4/3 x (fma.f64 -1/241920 (pow.f64 x 7) (fma.f64 1/1440 (pow.f64 x 5) (*.f64 (pow.f64 x 3) -1/18))))
(fma.f64 x 4/3 (fma.f64 (pow.f64 x 7) -1/241920 (fma.f64 (pow.f64 x 3) -1/18 (*.f64 (pow.f64 x 5) 1/1440))))
(fma.f64 x 4/3 (fma.f64 (pow.f64 x 3) -1/18 (fma.f64 (pow.f64 x 5) 1/1440 (*.f64 (pow.f64 x 7) -1/241920))))
(fma.f64 x 4/3 (fma.f64 (pow.f64 x 3) -1/18 (fma.f64 (pow.f64 x 7) -1/241920 (*.f64 (pow.f64 x 5) 1/1440))))
(fma.f64 (pow.f64 x 3) -1/18 (fma.f64 (pow.f64 x 7) -1/241920 (fma.f64 (pow.f64 x 5) 1/1440 (*.f64 x 4/3))))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(*.f64 2/3 (pow.f64 x 2))
(.f64 2/3 (.f64 x x))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (.f64 2/3 (pow.f64 x 2)))
(fma.f64 -1/18 (pow.f64 x 4) (.f64 2/3 (.f64 x x)))
(fma.f64 2/3 (.f64 x x) (.f64 -1/18 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/18) 2/3)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (*.f64 1/540 (pow.f64 x 6))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (.f64 1/540 (pow.f64 x 6))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 1/540 (pow.f64 x 6) (.f64 2/3 (.f64 x x))))
(fma.f64 2/3 (.f64 x x) (fma.f64 -1/18 (pow.f64 x 4) (.f64 1/540 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/18) 2/3) (*.f64 1/540 (pow.f64 x 6)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (+.f64 (.f64 -1/30240 (pow.f64 x 8)) (.f64 1/540 (pow.f64 x 6)))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (fma.f64 -1/30240 (pow.f64 x 8) (.f64 1/540 (pow.f64 x 6)))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (fma.f64 1/540 (pow.f64 x 6) (.f64 -1/30240 (pow.f64 x 8)))))
(fma.f64 2/3 (.f64 x x) (fma.f64 -1/18 (pow.f64 x 4) (fma.f64 1/540 (pow.f64 x 6) (.f64 -1/30240 (pow.f64 x 8)))))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))

eval103.0ms (1.3%)

Compiler: Compiled 4336 to 3154 computations (27.3% saved)

prune77.0ms (1%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	233	32	265
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	235	32	267

Error

0.0b

Counts

267 → 32

Alt Table

Click to see full alt table

Status	Error	Program
▶	36.3b	(*.f64 2/3 x)
	25.6b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
	21.3b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
	25.6b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
	33.3b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))))
	25.6b	(+.f64 0 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))
	0.6b	(.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
	11.2b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
	11.2b	(/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 2) (sin.f64 x))
	1.5b	(.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
	21.2b	(/.f64 (pow.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 6) 1/3) (sin.f64 x))
	11.1b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
	1.4b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 x))))
	21.1b	(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6)) (/.f64 8/3 (sin.f64 x)))
	25.7b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	25.8b	(/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))))) 1) (sin.f64 x))
▶	25.6b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
▶	33.4b	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
	0.5b	(.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 1) (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
	47.0b	(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
	36.9b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
	33.4b	(pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)
	25.6b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
	36.8b	(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
	26.3b	(log1p.f64 (expm1.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))
▶	25.7b	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
▶	0.5b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
	25.7b	(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
	47.1b	(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
	25.7b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
	11.3b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (*.f64 (/.f64 1 (sin.f64 x)) 8/3))
	11.2b	(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 914 to 748 computations (18.2% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))
✓	0.3b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
✓	0.3b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))
1.0ms	x	@	inf	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))
0.0ms	x	@	0	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))
0.0ms	x	@	0	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	0	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))

rewrite85.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

544×	`log-prod_binary64`
418×	`exp-prod_binary64`
290×	`pow-prod-down_binary64`
269×	`pow2_binary64`
198×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	209	40
2	2665	40

Stop Event

1×	node limit

Counts

3 → 122

Calls

Call 1

Inputs
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (sin.f64 (*.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (sin.f64 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (sin.f64 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 64/9 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) 2)) (cbrt.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))) (sqrt.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 64/9 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8/3) (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) 1) 1))))))

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((x pow.f64 (pow.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) 3) (pow.f64 (sin.f64 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))))) 2)) (cbrt.f64 (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))) (sqrt.f64 (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 64/9 (pow.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8/3) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) 3) (pow.f64 (sin.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 8/3 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) 1) (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))))))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

762×	`distribute-lft-out_binary64`
724×	`fma-def_binary64`
518×	`unswap-sqr_binary64`
495×	`associate-l_binary64`
399×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	486
1	152	484
2	362	482
3	1035	482
4	3327	482
5	5268	482
6	7949	482

Stop Event

1×	node limit

Counts

158 → 150

Calls

Call 1

Inputs
(*.f64 4/3 x)
(+.f64 (.f64 4/3 x) (.f64 -1/18 (pow.f64 x 3)))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (*.f64 -1/18 (pow.f64 x 3))))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 -1/241920 (pow.f64 x 7)) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (.f64 -1/18 (pow.f64 x 3)))))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
4/3
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 4/3)
(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 4/3 (.f64 5/288 (pow.f64 x 4))))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 4/3 (+.f64 (.f64 5/288 (pow.f64 x 4)) (*.f64 61/34560 (pow.f64 x 6)))))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))

Outputs
(*.f64 4/3 x)
(+.f64 (.f64 4/3 x) (.f64 -1/18 (pow.f64 x 3)))
(fma.f64 4/3 x (*.f64 -1/18 (pow.f64 x 3)))
(fma.f64 -1/18 (pow.f64 x 3) (*.f64 4/3 x))
(.f64 x (fma.f64 x (.f64 x -1/18) 4/3))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (*.f64 -1/18 (pow.f64 x 3))))
(fma.f64 4/3 x (fma.f64 1/1440 (pow.f64 x 5) (*.f64 -1/18 (pow.f64 x 3))))
(fma.f64 4/3 x (fma.f64 -1/18 (pow.f64 x 3) (*.f64 1/1440 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x -1/18) 4/3) (.f64 1/1440 (pow.f64 x 5)))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 -1/241920 (pow.f64 x 7)) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (.f64 -1/18 (pow.f64 x 3)))))
(fma.f64 4/3 x (fma.f64 -1/241920 (pow.f64 x 7) (fma.f64 1/1440 (pow.f64 x 5) (*.f64 -1/18 (pow.f64 x 3)))))
(fma.f64 4/3 x (fma.f64 -1/241920 (pow.f64 x 7) (fma.f64 -1/18 (pow.f64 x 3) (*.f64 1/1440 (pow.f64 x 5)))))
(fma.f64 4/3 x (fma.f64 1/1440 (pow.f64 x 5) (fma.f64 -1/241920 (pow.f64 x 7) (*.f64 -1/18 (pow.f64 x 3)))))
(fma.f64 x (fma.f64 x (.f64 x -1/18) 4/3) (fma.f64 1/1440 (pow.f64 x 5) (.f64 -1/241920 (pow.f64 x 7))))
(fma.f64 -1/18 (pow.f64 x 3) (fma.f64 1/1440 (pow.f64 x 5) (fma.f64 -1/241920 (pow.f64 x 7) (*.f64 4/3 x))))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(.f64 8/3 (sin.f64 (.f64 1/2 x)))
(.f64 8/3 (sin.f64 (.f64 x 1/2)))
(*.f64 2/3 x)
(*.f64 x 2/3)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 x 2/3))
(fma.f64 x 2/3 (*.f64 (pow.f64 x 3) 1/18))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 (pow.f64 x 5) 1/180)))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 x 2/3 (*.f64 (pow.f64 x 5) 1/180)))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 3) 1/18 (*.f64 (pow.f64 x 5) 1/180)))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (.f64 (pow.f64 x 5) 1/180))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 5) 1/180 (*.f64 x 2/3)))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 5) 1/180 (*.f64 (pow.f64 x 3) 1/18)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 (pow.f64 x 5) 1/180))))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 7) 17/30240 (fma.f64 x 2/3 (*.f64 (pow.f64 x 5) 1/180))))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 5) 1/180 (fma.f64 x 2/3 (*.f64 (pow.f64 x 7) 17/30240))))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 5) 1/180 (*.f64 (pow.f64 x 7) 17/30240))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (fma.f64 (pow.f64 x 5) 1/180 (.f64 (pow.f64 x 7) 17/30240)))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 5) 1/180 (fma.f64 (pow.f64 x 7) 17/30240 (*.f64 (pow.f64 x 3) 1/18))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
4/3
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 4/3)
(fma.f64 1/6 (*.f64 x x) 4/3)
(fma.f64 x (*.f64 x 1/6) 4/3)
(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 4/3 (.f64 5/288 (pow.f64 x 4))))
(+.f64 (fma.f64 1/6 (.f64 x x) 4/3) (.f64 5/288 (pow.f64 x 4)))
(fma.f64 1/6 (*.f64 x x) (fma.f64 5/288 (pow.f64 x 4) 4/3))
(fma.f64 x (*.f64 x 1/6) (fma.f64 5/288 (pow.f64 x 4) 4/3))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/288 1/6) 4/3)
(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 4/3 (+.f64 (.f64 5/288 (pow.f64 x 4)) (*.f64 61/34560 (pow.f64 x 6)))))
(+.f64 (fma.f64 1/6 (.f64 x x) 4/3) (fma.f64 5/288 (pow.f64 x 4) (.f64 61/34560 (pow.f64 x 6))))
(fma.f64 x (*.f64 x 1/6) (fma.f64 5/288 (pow.f64 x 4) (fma.f64 61/34560 (pow.f64 x 6) 4/3)))
(fma.f64 5/288 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/6) (fma.f64 61/34560 (pow.f64 x 6) 4/3)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/288 1/6) (fma.f64 61/34560 (pow.f64 x 6) 4/3))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (sin.f64 x) 8/3))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 2/3 x)

Compiler

Compiled 6 to 4 computations (33.3% saved)

series5.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(*.f64 2/3 x)
2.0ms	x	@	0	(*.f64 2/3 x)
0.0ms	x	@	-inf	(*.f64 2/3 x)

rewrite52.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

345×	`pow1_binary64`
338×	`add-sqr-sqrt_binary64`
329×	`*-un-lft-identity_binary64`
321×	`add-log-exp_binary64`
321×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	80	4
2	873	4

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 2/3 x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (*.f64 2/3 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 2/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (exp.f64 x))) (log.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 4/3) x))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2/3) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 2/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (*.f64 2/3 x)) 3) 1) (+.f64 (*.f64 (+.f64 1 (*.f64 2/3 x)) (+.f64 1 (*.f64 2/3 x))) (+.f64 1 (*.f64 (+.f64 1 (*.f64 2/3 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (*.f64 2/3 x)) (+.f64 1 (*.f64 2/3 x))) 1) (+.f64 (+.f64 1 (*.f64 2/3 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2/3 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 8/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 2/3 x)))) (sqrt.f64 (log.f64 (*.f64 2/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 2/3 x))) 2)) (cbrt.f64 (log.f64 (*.f64 2/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 2/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) 8/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 2/3 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2/3 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2/3 x))) 2))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

Calls

Call 1

Inputs

Outputs

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sin.f64 x))
✓	0.2b	(.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x)))
✓	0.3b	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
✓	2.6b	(-.f64 1/2 (*.f64 1/2 (cos.f64 x)))

Compiler

Compiled 47 to 30 computations (36.2% saved)

series6.0ms (0.1%)

Counts

4 → 32

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
1.0ms	x	@	-inf	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
1.0ms	x	@	-inf	(/.f64 1 (sin.f64 x))
1.0ms	x	@	0	(-.f64 1/2 (*.f64 1/2 (cos.f64 x)))
1.0ms	x	@	inf	(/.f64 1 (sin.f64 x))

rewrite91.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`log-prod_binary64`
318×	`pow-prod-down_binary64`
313×	`pow2_binary64`
219×	`pow1/3_binary64`
219×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	259	46
2	3226	40

Stop Event

1×	node limit

Counts

4 → 164

Calls

Call 1

Inputs
(-.f64 1/2 (*.f64 1/2 (cos.f64 x)))
(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x)))
(/.f64 1 (sin.f64 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (.f64 (cos.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (.f64 (.f64 (cos.f64 x) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 (cos.f64 x) -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 x) -1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 x) -1/2 1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (cos.f64 x) -1/2 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (cos.f64 x) -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 2) (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 2) (.f64 (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) (.f64 (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3))) (/.f64 1 (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2))) (/.f64 1 (fma.f64 1/2 (cos.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4) (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/2 (cos.f64 x) 1/2) (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3))) (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2))) (fma.f64 1/2 (cos.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3)))) (neg.f64 (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2)))) (neg.f64 (fma.f64 1/2 (cos.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3))) 1) (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2))) 1) (fma.f64 1/2 (cos.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 (.f64 (cos.f64 x) -1/2) 3)) (+.f64 1/4 (-.f64 (pow.f64 (.f64 (cos.f64 x) -1/2) 2) (.f64 1/2 (.f64 (cos.f64 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (.f64 (cos.f64 x) -1/2) 2)) (-.f64 1/2 (.f64 (cos.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4) (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 1/2 (cos.f64 x) 1/2) (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 (cos.f64 x) -1/2 1/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (neg.f64 (cos.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 x) -1/2 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (cos.f64 x) -1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (cos.f64 x))) 2) (neg.f64 (cbrt.f64 (.f64 1/2 (cos.f64 x)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 1/2 (cos.f64 x))) (neg.f64 (sqrt.f64 (.f64 1/2 (cos.f64 x)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (.f64 1/2 (cos.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (cos.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 x) -1/2)) 2) (cbrt.f64 (.f64 (cos.f64 x) -1/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (cos.f64 x) -1/2)) (sqrt.f64 (.f64 (cos.f64 x) -1/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cos.f64 x)) 1/2 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (cos.f64 x))) 2)) (cbrt.f64 (.f64 1/2 (cos.f64 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (.f64 1/2 (cos.f64 x)))) (sqrt.f64 (.f64 1/2 (cos.f64 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/2 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/2 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1/2)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 8/3) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 8/3) 1) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 8/3) -1) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 2) 64/9) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 2) 64/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (/.f64 1 (sin.f64 x))) (.f64 (.f64 (cos.f64 x) -1/2) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1 (sin.f64 x)) 1/2) (.f64 (/.f64 1 (sin.f64 x)) (.f64 (cos.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 3) (pow.f64 (sin.f64 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (fma.f64 (cos.f64 x) -1/2 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 3) (pow.f64 (sin.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (sin.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (sin.f64 x))) (cbrt.f64 (pow.f64 (sin.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (sin.f64 x) -2)) (/.f64 1 (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sin.f64 x) -1/2) (pow.f64 (sin.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (sin.f64 x)) -2) (/.f64 1 (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sin.f64 x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sin.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sin.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (sin.f64 x) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 (cbrt.f64 (sin.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -1/2 (log.f64 (sin.f64 x))) 2))))))

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

825×	`distribute-rgt-out_binary64`
745×	`associate-r_binary64`
692×	`unswap-sqr_binary64`
591×	`distribute-lft-in_binary64`
317×	`fma-def_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	73	483
1	183	483
2	453	443
3	1355	443
4	3213	443
5	6127	379
6	7542	379

Stop Event

1×	node limit

Counts

196 → 198

Calls

Call 1

Inputs
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(*.f64 1/4 x)
(+.f64 (.f64 1/48 (pow.f64 x 3)) (.f64 1/4 x))
(+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (*.f64 1/4 x)))
(+.f64 (.f64 17/80640 (pow.f64 x 7)) (+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (.f64 1/4 x))))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 1 x)
(+.f64 (*.f64 1/6 x) (/.f64 1 x))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 7/360 (pow.f64 x 3)) (/.f64 1 x)))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 31/15120 (pow.f64 x 5)) (+.f64 (*.f64 7/360 (pow.f64 x 3)) (/.f64 1 x))))

Outputs
(*.f64 1/4 (pow.f64 x 2))
(.f64 1/4 (.f64 x x))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 1/4 (.f64 x x) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 -1/48 (pow.f64 x 4) (.f64 1/4 (.f64 x x)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 -1/48 (pow.f64 x 4) (fma.f64 1/1440 (pow.f64 x 6) (.f64 1/4 (.f64 x x))))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 -1/48 (pow.f64 x 4) (fma.f64 1/1440 (pow.f64 x 6) (.f64 1/4 (.f64 x x)))))
(*.f64 2/3 x)
(*.f64 x 2/3)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 x 2/3))
(fma.f64 x 2/3 (*.f64 1/18 (pow.f64 x 3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 x 2/3 (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 x 2/3 (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 x 2/3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 x 2/3 (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 x 2/3 (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 x 2/3 (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (-.f64 4/3 (*.f64 4/3 (cos.f64 x))) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 1/4 x)
(+.f64 (.f64 1/48 (pow.f64 x 3)) (.f64 1/4 x))
(fma.f64 1/48 (pow.f64 x 3) (*.f64 1/4 x))
(fma.f64 1/4 x (*.f64 (pow.f64 x 3) 1/48))
(+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (*.f64 1/4 x)))
(fma.f64 1/48 (pow.f64 x 3) (fma.f64 1/480 (pow.f64 x 5) (*.f64 1/4 x)))
(fma.f64 (pow.f64 x 3) 1/48 (fma.f64 1/4 x (*.f64 (pow.f64 x 5) 1/480)))
(fma.f64 1/4 x (fma.f64 (pow.f64 x 3) 1/48 (*.f64 (pow.f64 x 5) 1/480)))
(+.f64 (.f64 17/80640 (pow.f64 x 7)) (+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (.f64 1/4 x))))
(fma.f64 17/80640 (pow.f64 x 7) (fma.f64 1/48 (pow.f64 x 3) (fma.f64 1/480 (pow.f64 x 5) (*.f64 1/4 x))))
(fma.f64 (pow.f64 x 7) 17/80640 (fma.f64 (pow.f64 x 3) 1/48 (fma.f64 1/4 x (*.f64 (pow.f64 x 5) 1/480))))
(fma.f64 (pow.f64 x 3) 1/48 (fma.f64 (pow.f64 x 7) 17/80640 (fma.f64 1/4 x (*.f64 (pow.f64 x 5) 1/480))))
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))
(/.f64 (+.f64 1/2 (*.f64 (cos.f64 x) -1/2)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 1/2)
(/.f64 1 x)
(+.f64 (*.f64 1/6 x) (/.f64 1 x))
(fma.f64 1/6 x (/.f64 1 x))
(fma.f64 x 1/6 (/.f64 1 x))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 7/360 (pow.f64 x 3)) (/.f64 1 x)))
(fma.f64 1/6 x (fma.f64 7/360 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/6 (fma.f64 (pow.f64 x 3) 7/360 (/.f64 1 x)))
(fma.f64 (pow.f64 x 3) 7/360 (fma.f64 x 1/6 (/.f64 1 x)))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 31/15120 (pow.f64 x 5)) (+.f64 (*.f64 7/360 (pow.f64 x 3)) (/.f64 1 x))))
(fma.f64 1/6 x (fma.f64 31/15120 (pow.f64 x 5) (fma.f64 7/360 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 x 1/6 (fma.f64 (pow.f64 x 5) 31/15120 (fma.f64 (pow.f64 x 3) 7/360 (/.f64 1 x))))
(fma.f64 (pow.f64 x 5) 31/15120 (fma.f64 (pow.f64 x 3) 7/360 (fma.f64 x 1/6 (/.f64 1 x))))
(fma.f64 x 1/6 (fma.f64 (pow.f64 x 3) 7/360 (fma.f64 (pow.f64 x 5) 31/15120 (/.f64 1 x))))

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
✓	0.2b	(.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x)))))
✓	0.2b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
	2.6b	(-.f64 1/2 (*.f64 1/2 (cos.f64 x)))

Compiler

Compiled 52 to 33 computations (36.5% saved)

series8.0ms (0.1%)

Counts

3 → 20

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
2.0ms	x	@	-inf	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
1.0ms	x	@	inf	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
1.0ms	x	@	0	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
0.0ms	x	@	0	(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))

rewrite82.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`log-prod_binary64`
335×	`pow2_binary64`
302×	`pow-prod-down_binary64`
230×	`pow1/3_binary64`
230×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	268	48
2	3397	42

Stop Event

1×	node limit

Counts

3 → 96

Calls

Call 1

Inputs

(pow.f64 (*.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) -1)

(*.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))

(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) -2)) (cbrt.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) (sqrt.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 3/8 (sin.f64 x))) (fma.f64 (cos.f64 x) -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))) -2) (cbrt.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (/.f64 (sin.f64 x) (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 3/8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) (sqrt.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))) -2) (cbrt.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8/3) (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8/3 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 3/8 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (*.f64 3/8 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 3/8 (sin.f64 x))) (neg.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) 1) (fma.f64 (cos.f64 x) -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 2))) (cbrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2))) (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sin.f64 x)) 3/8) (neg.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 3/8 (neg.f64 (sin.f64 x))) (neg.f64 (fma.f64 (cos.f64 x) -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (*.f64 3/8 (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 3/8 (sin.f64 x)) (fma.f64 (cos.f64 x) -1/2 1/2))) 1))))))

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

simplify106.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-neg_binary64`
741×	`fma-def_binary64`
610×	`associate-l_binary64`
428×	`associate-r_binary64`
236×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	60	294
1	150	292
2	356	268
3	920	252
4	1667	252
5	3355	228
6	4122	228
7	4793	228
8	5766	228
9	6914	228

Stop Event

1×	node limit

Counts

116 → 119

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(/.f64 3/2 x)
(+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (*.f64 3/2 (/.f64 1 x))))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 -1/20160 (pow.f64 x 5)))))
(/.f64 4 x)
(+.f64 (.f64 -1/3 x) (.f64 4 (/.f64 1 x)))
(+.f64 (.f64 -1/180 (pow.f64 x 3)) (+.f64 (.f64 -1/3 x) (*.f64 4 (/.f64 1 x))))
(+.f64 (.f64 -1/180 (pow.f64 x 3)) (+.f64 (.f64 -1/3 x) (+.f64 (.f64 -1/7560 (pow.f64 x 5)) (.f64 4 (/.f64 1 x)))))

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 1/18 (pow.f64 x 3)))))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 8/3 (/.f64 (+.f64 1/2 (.f64 (cos.f64 x) -1/2)) (sin.f64 x)))
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(/.f64 (fma.f64 (cos.f64 x) -4/3 4/3) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(/.f64 3/2 x)
(+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))
(fma.f64 -1/8 x (/.f64 3/2 x))
(fma.f64 x -1/8 (/.f64 3/2 x))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (*.f64 3/2 (/.f64 1 x))))
(fma.f64 -1/8 x (fma.f64 -1/480 (pow.f64 x 3) (/.f64 3/2 x)))
(fma.f64 x -1/8 (fma.f64 (pow.f64 x 3) -1/480 (/.f64 3/2 x)))
(fma.f64 x (fma.f64 -1/480 (*.f64 x x) -1/8) (/.f64 3/2 x))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 -1/20160 (pow.f64 x 5)))))
(fma.f64 -1/8 x (fma.f64 -1/480 (pow.f64 x 3) (+.f64 (/.f64 3/2 x) (*.f64 (pow.f64 x 5) -1/20160))))
(fma.f64 x -1/8 (fma.f64 (pow.f64 x 3) -1/480 (fma.f64 (pow.f64 x 5) -1/20160 (/.f64 3/2 x))))
(fma.f64 x (fma.f64 -1/480 (*.f64 x x) -1/8) (fma.f64 (pow.f64 x 5) -1/20160 (/.f64 3/2 x)))
(/.f64 4 x)
(+.f64 (.f64 -1/3 x) (.f64 4 (/.f64 1 x)))
(fma.f64 -1/3 x (/.f64 4 x))
(fma.f64 x -1/3 (/.f64 4 x))
(+.f64 (.f64 -1/180 (pow.f64 x 3)) (+.f64 (.f64 -1/3 x) (*.f64 4 (/.f64 1 x))))
(fma.f64 -1/180 (pow.f64 x 3) (fma.f64 -1/3 x (/.f64 4 x)))
(fma.f64 (pow.f64 x 3) -1/180 (fma.f64 x -1/3 (/.f64 4 x)))
(fma.f64 x -1/3 (fma.f64 (pow.f64 x 3) -1/180 (/.f64 4 x)))
(fma.f64 x (fma.f64 x (*.f64 x -1/180) -1/3) (/.f64 4 x))
(+.f64 (.f64 -1/180 (pow.f64 x 3)) (+.f64 (.f64 -1/3 x) (+.f64 (.f64 -1/7560 (pow.f64 x 5)) (.f64 4 (/.f64 1 x)))))
(fma.f64 -1/180 (pow.f64 x 3) (fma.f64 -1/3 x (fma.f64 -1/7560 (pow.f64 x 5) (/.f64 4 x))))
(fma.f64 (pow.f64 x 3) -1/180 (fma.f64 x -1/3 (fma.f64 (pow.f64 x 5) -1/7560 (/.f64 4 x))))
(fma.f64 x (fma.f64 x (*.f64 x -1/180) -1/3) (fma.f64 (pow.f64 x 5) -1/7560 (/.f64 4 x)))
(fma.f64 x -1/3 (fma.f64 (pow.f64 x 5) -1/7560 (fma.f64 (pow.f64 x 3) -1/180 (/.f64 4 x))))

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (sin.f64 x))
✓	0.1b	(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))
✓	0.2b	(/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x)))
✓	0.3b	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)

Compiler

Compiled 50 to 35 computations (30% saved)

series13.0ms (0.2%)

Counts

4 → 28

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
2.0ms	x	@	-inf	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
2.0ms	x	@	inf	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
1.0ms	x	@	0	(/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x)))
1.0ms	x	@	0	(sqrt.f64 (sin.f64 x))

rewrite99.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`log-prod_binary64`
335×	`pow-prod-down_binary64`
313×	`pow2_binary64`
220×	`pow-unpow_binary64`
219×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	269	51
2	3119	51

Stop Event

1×	node limit

Counts

4 → 155

Calls

Call 1

Inputs
(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
(/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))
(sqrt.f64 (sin.f64 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (.f64 (pow.f64 (sin.f64 x) -1/2) (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (.f64 x 1/2))) (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (pow.f64 (sin.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))) 2) (cbrt.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)) 1/4) (pow.f64 (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (.f64 x 1/2))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))) (pow.f64 (sin.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (.f64 x 1/2))) 3/2) (pow.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)) 5/6) (pow.f64 (/.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (pow.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (sin.f64 (.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 8/3) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))) (/.f64 (sqrt.f64 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 8/3) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (sin.f64 (.f64 x 1/2))) (/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 x)) (/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (.f64 x 1/2))) (/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (sqrt.f64 8/3))) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2)))) (neg.f64 (sqrt.f64 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (sqrt.f64 8/3))) 2) (pow.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 8/3)) (.f64 (sqrt.f64 (sin.f64 x)) (/.f64 (sqrt.f64 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (sqrt.f64 8/3))) (sqrt.f64 8/3)) (.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (/.f64 (sqrt.f64 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))))))) 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(/.f64 (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))))) -1))))))
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (sin.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sin.f64 x) 1/6) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sin.f64 x) 1/4) (pow.f64 (sin.f64 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sin.f64 x)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sin.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3/2 (log.f64 (sin.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (sin.f64 x) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/4 (log.f64 (sin.f64 x))) 2))))))

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

589×	`unswap-sqr_binary64`
567×	`distribute-lft-out_binary64`
550×	`fma-def_binary64`
537×	`associate-l_binary64`
414×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	540
1	102	500
2	245	490
3	819	474
4	3253	474
5	5508	474
6	6398	474

Stop Event

1×	node limit

Counts

183 → 168

Calls

Call 1

Inputs
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 1/2 (.f64 (sqrt.f64 8/3) x))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 8/3) x)) (.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3))))
(+.f64 (.f64 1/3840 (.f64 (sqrt.f64 8/3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 8/3) x)) (.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3)))))
(+.f64 (.f64 1/3840 (.f64 (sqrt.f64 8/3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 8/3) x)) (+.f64 (.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3))) (.f64 -1/645120 (.f64 (sqrt.f64 8/3) (pow.f64 x 7))))))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))

Outputs
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(/.f64 (.f64 (pow.f64 (sqrt.f64 8/3) 2) (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2)) (sin.f64 x))
(.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 (sqrt.f64 (/.f64 1 (sin.f64 x))) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 1 (sin.f64 x)))))
(.f64 1/2 (.f64 (sqrt.f64 8/3) x))
(.f64 (sqrt.f64 8/3) (.f64 1/2 x))
(.f64 x (.f64 (sqrt.f64 8/3) 1/2))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 8/3) x)) (.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3))))
(fma.f64 1/2 (.f64 (sqrt.f64 8/3) x) (.f64 -1/48 (*.f64 (sqrt.f64 8/3) (pow.f64 x 3))))
(fma.f64 1/2 (.f64 (sqrt.f64 8/3) x) (.f64 (sqrt.f64 8/3) (*.f64 (pow.f64 x 3) -1/48)))
(.f64 (sqrt.f64 8/3) (+.f64 (.f64 1/2 x) (*.f64 -1/48 (pow.f64 x 3))))
(.f64 (sqrt.f64 8/3) (fma.f64 1/2 x (.f64 -1/48 (pow.f64 x 3))))
(.f64 (sqrt.f64 8/3) (fma.f64 -1/48 (pow.f64 x 3) (.f64 1/2 x)))
(+.f64 (.f64 1/3840 (.f64 (sqrt.f64 8/3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 8/3) x)) (.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3)))))
(fma.f64 1/3840 (.f64 (sqrt.f64 8/3) (pow.f64 x 5)) (fma.f64 1/2 (.f64 (sqrt.f64 8/3) x) (.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3)))))
(fma.f64 1/3840 (.f64 (sqrt.f64 8/3) (pow.f64 x 5)) (fma.f64 1/2 (.f64 (sqrt.f64 8/3) x) (.f64 (sqrt.f64 8/3) (.f64 (pow.f64 x 3) -1/48))))
(fma.f64 (sqrt.f64 8/3) (.f64 1/2 x) (.f64 (sqrt.f64 8/3) (+.f64 (.f64 -1/48 (pow.f64 x 3)) (.f64 1/3840 (pow.f64 x 5)))))
(.f64 (sqrt.f64 8/3) (+.f64 (.f64 -1/48 (pow.f64 x 3)) (fma.f64 1/2 x (*.f64 1/3840 (pow.f64 x 5)))))
(.f64 (sqrt.f64 8/3) (+.f64 (.f64 1/2 x) (fma.f64 -1/48 (pow.f64 x 3) (*.f64 1/3840 (pow.f64 x 5)))))
(+.f64 (.f64 1/3840 (.f64 (sqrt.f64 8/3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 8/3) x)) (+.f64 (.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3))) (.f64 -1/645120 (.f64 (sqrt.f64 8/3) (pow.f64 x 7))))))
(fma.f64 1/3840 (.f64 (sqrt.f64 8/3) (pow.f64 x 5)) (fma.f64 1/2 (.f64 (sqrt.f64 8/3) x) (fma.f64 -1/48 (.f64 (sqrt.f64 8/3) (pow.f64 x 3)) (.f64 -1/645120 (*.f64 (sqrt.f64 8/3) (pow.f64 x 7))))))
(+.f64 (.f64 (sqrt.f64 8/3) (+.f64 (.f64 1/2 x) (.f64 -1/48 (pow.f64 x 3)))) (.f64 (sqrt.f64 8/3) (+.f64 (.f64 -1/645120 (pow.f64 x 7)) (.f64 1/3840 (pow.f64 x 5)))))
(.f64 (sqrt.f64 8/3) (+.f64 (fma.f64 -1/48 (pow.f64 x 3) (.f64 -1/645120 (pow.f64 x 7))) (fma.f64 1/2 x (*.f64 1/3840 (pow.f64 x 5)))))
(.f64 (sqrt.f64 8/3) (+.f64 (fma.f64 1/2 x (.f64 1/3840 (pow.f64 x 5))) (fma.f64 -1/48 (pow.f64 x 3) (*.f64 -1/645120 (pow.f64 x 7)))))
(.f64 (sqrt.f64 8/3) (+.f64 (fma.f64 -1/645120 (pow.f64 x 7) (.f64 1/3840 (pow.f64 x 5))) (fma.f64 -1/48 (pow.f64 x 3) (*.f64 1/2 x))))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 8/3) (sin.f64 (.f64 1/2 x)))

eval374.0ms (4.7%)

Compiler: Compiled 12630 to 9161 computations (27.5% saved)

prune209.0ms (2.6%)

Pruning

26 alts after pruning (22 fresh and 4 done)

	Pruned	Kept	Total
New	713	12	725
Fresh	17	10	27
Picked	1	0	1
Done	0	4	4
Total	731	26	757

Error

Counts

757 → 26

Alt Table

Click to see full alt table

Status	Error	Program
✓	36.3b	(*.f64 2/3 x)
	25.6b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
	36.8b	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
▶	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
	25.6b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
	49.2b	(fabs.f64 (*.f64 2/3 x))
▶	25.7b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
	50.4b	(pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)
	11.2b	(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
	0.4b	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
	36.8b	(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
▶	11.1b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
	0.5b	(.f64 (.f64 8/3 (/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))) (sin.f64 (.f64 x 1/2)))
	21.1b	(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6)) (/.f64 8/3 (sin.f64 x)))
	1.4b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 x))))
	25.7b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
✓	25.6b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
	25.6b	(/.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 3/8)
▶	60.5b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
✓	25.7b	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
▶	36.5b	(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)
	11.2b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
	36.3b	(pow.f64 (/.f64 3/2 x) -1)
	60.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
	25.6b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
✓	0.5b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))

Compiler

Compiled 561 to 463 computations (17.5% saved)

localize41.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))
✓	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
✓	0.2b	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))

Compiler

Compiled 43 to 29 computations (32.6% saved)

series8.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
1.0ms	x	@	0	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
1.0ms	x	@	inf	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
1.0ms	x	@	inf	(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))
0.0ms	x	@	-inf	(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))

rewrite84.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log-prod_binary64`
432×	`exp-prod_binary64`
277×	`pow-prod-down_binary64`
277×	`pow2_binary64`
194×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	47
1	214	45
2	2801	45

Stop Event

1×	node limit

Counts

3 → 139

Calls

Call 1

Inputs
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))

Outputs

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(*.f64 (cbrt.f64 (sin.f64 x)) (/.f64 1 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) 2) (cbrt.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (/.f64 1 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) (sqrt.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sin.f64 x)) (/.f64 1 (neg.f64 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) (/.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (cbrt.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) -2)) (/.f64 1 (cbrt.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 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(*.f64 x 1/2))) 2) 3/8) (/.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)) -2) (/.f64 (sin.f64 (*.f64 x 1/2)) (cbrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)) 2)) (/.f64 1 (cbrt.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)) 2)) (/.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8) -1/2) (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))) (/.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) 3/8)) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (sin.f64 x)) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 8/3) 1) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (neg.f64 (sin.f64 x))) (neg.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 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3) (pow.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) 2)) (cbrt.f64 (neg.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (sqrt.f64 (neg.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) (pow.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 3/8) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 3/8) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 3/8) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 3/8) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 3/8 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 x) 3/8) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sin.f64 x) 3/8)) (neg.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) 1) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2)) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sin.f64 x) 3/8) (sqrt.f64 (sin.f64 (*.f64 x 1/2)))) (sqrt.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sin.f64 x)) 3/8) (neg.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 3/8 (neg.f64 (sin.f64 x))) (neg.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 9/64 (pow.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 x) 3/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))) 2)) (cbrt.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)))) (sqrt.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 9/64 (pow.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 3/8) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8)) 1) 1))))))

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
595×	`associate-l_binary64`
518×	`unswap-sqr_binary64`
472×	`distribute-rgt-out_binary64`
467×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	498
1	139	488
2	334	486
3	1012	486
4	3927	486
5	6505	486

Stop Event

1×	node limit

Counts

175 → 167

Calls

Call 1

Inputs
2
(+.f64 2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (.f64 -1/4 (pow.f64 x 2))))
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 -1/23040 (pow.f64 x 6)))))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
3/4
(+.f64 3/4 (*.f64 -3/32 (pow.f64 x 2)))
(+.f64 (.f64 1/512 (pow.f64 x 4)) (+.f64 3/4 (.f64 -3/32 (pow.f64 x 2))))
(+.f64 (.f64 -1/61440 (pow.f64 x 6)) (+.f64 (.f64 1/512 (pow.f64 x 4)) (+.f64 3/4 (*.f64 -3/32 (pow.f64 x 2)))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))

Outputs
2
(+.f64 2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 2 (.f64 -1/4 (.f64 x x)))
(fma.f64 -1/4 (*.f64 x x) 2)
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (.f64 -1/4 (pow.f64 x 2))))
(fma.f64 1/192 (pow.f64 x 4) (+.f64 2 (.f64 -1/4 (.f64 x x))))
(fma.f64 1/192 (pow.f64 x 4) (fma.f64 -1/4 (*.f64 x x) 2))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/192) -1/4) 2)
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 -1/23040 (pow.f64 x 6)))))
(fma.f64 1/192 (pow.f64 x 4) (+.f64 2 (fma.f64 -1/4 (.f64 x x) (.f64 -1/23040 (pow.f64 x 6)))))
(+.f64 (fma.f64 1/192 (pow.f64 x 4) (fma.f64 -1/4 (.f64 x x) 2)) (.f64 -1/23040 (pow.f64 x 6)))
(fma.f64 1/192 (pow.f64 x 4) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -1/23040 (pow.f64 x 6) 2)))
(fma.f64 -1/4 (*.f64 x x) (fma.f64 1/192 (pow.f64 x 4) (fma.f64 -1/23040 (pow.f64 x 6) 2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(*.f64 2/3 x)
(*.f64 x 2/3)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 x 2/3))
(fma.f64 x 2/3 (*.f64 1/18 (pow.f64 x 3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 x 2/3 (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 x 2/3 (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 x 2/3 (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 x 2/3))))
(fma.f64 x 2/3 (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 1/18 (pow.f64 x 3)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 8/3 (/.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
3/4
(+.f64 3/4 (*.f64 -3/32 (pow.f64 x 2)))
(+.f64 3/4 (.f64 (.f64 x x) -3/32))
(fma.f64 (*.f64 x x) -3/32 3/4)
(fma.f64 x (*.f64 x -3/32) 3/4)
(+.f64 (.f64 1/512 (pow.f64 x 4)) (+.f64 3/4 (.f64 -3/32 (pow.f64 x 2))))
(fma.f64 1/512 (pow.f64 x 4) (+.f64 3/4 (.f64 (.f64 x x) -3/32)))
(fma.f64 (pow.f64 x 4) 1/512 (fma.f64 (*.f64 x x) -3/32 3/4))
(fma.f64 x (*.f64 x -3/32) (fma.f64 (pow.f64 x 4) 1/512 3/4))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/512) -3/32) 3/4)
(+.f64 (.f64 -1/61440 (pow.f64 x 6)) (+.f64 (.f64 1/512 (pow.f64 x 4)) (+.f64 3/4 (*.f64 -3/32 (pow.f64 x 2)))))
(fma.f64 -1/61440 (pow.f64 x 6) (fma.f64 1/512 (pow.f64 x 4) (+.f64 3/4 (.f64 (.f64 x x) -3/32))))
(fma.f64 (pow.f64 x 6) -1/61440 (fma.f64 (pow.f64 x 4) 1/512 (fma.f64 (*.f64 x x) -3/32 3/4)))
(fma.f64 (pow.f64 x 4) 1/512 (fma.f64 (pow.f64 x 6) -1/61440 (fma.f64 x (*.f64 x -3/32) 3/4)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/512) -3/32) (fma.f64 (pow.f64 x 6) -1/61440 3/4))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))
(.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
(.f64 (sin.f64 x) (/.f64 3/8 (sin.f64 (.f64 x 1/2))))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(*.f64 2/3 x)
✓	3.7b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
0.0ms	x	@	0	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)

rewrite57.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`pow1_binary64`
684×	`add-log-exp_binary64`
684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
674×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	156	4
2	2109	4

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 2/3 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 2/3 x -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2/3 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2/3 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 2/3 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2/3 x -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2/3 x)) (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2) (cbrt.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2/3 x)) (sqrt.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) (+.f64 (*.f64 2/3 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) -1) (/.f64 1 (+.f64 (*.f64 2/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 2/3 x 1)) 1) (-.f64 (sqrt.f64 (fma.f64 2/3 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2/3 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) (+.f64 (*.f64 2/3 x) 2)) (+.f64 (pow.f64 (fma.f64 2/3 x 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 2/3 x) 2) (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) (+.f64 (*.f64 2/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) (-.f64 1 (*.f64 (fma.f64 2/3 x 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) -1) (+.f64 (*.f64 2/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) -1) (-.f64 (fma.f64 2/3 x 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) (+.f64 (*.f64 2/3 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2/3 x 1) 2) -1)) (neg.f64 (+.f64 (*.f64 2/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 2/3 x -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2/3 x -1) (fma.f64 2/3 x -1)) (fma.f64 2/3 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 2/3 x -1) (fma.f64 2/3 x -1))) (-.f64 1 (fma.f64 2/3 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8/27 (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 8/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 2/3 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2/3 x 1)) 2) (cbrt.f64 (fma.f64 2/3 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 2/3 x 1)) (sqrt.f64 (fma.f64 2/3 x 1)) -1)))))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

55 → 43

Calls

Call 1

Inputs
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)

Outputs
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)
✓	0.5b	(*.f64 3/8 (/.f64 4 x))

Compiler

Compiled 20 to 16 computations (20% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 3/8 (/.f64 4 x))
1.0ms	x	@	0	(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)
0.0ms	x	@	-inf	(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)
0.0ms	x	@	inf	(*.f64 3/8 (/.f64 4 x))
0.0ms	x	@	inf	(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)

rewrite65.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

750×	`pow1_binary64`
712×	`add-log-exp_binary64`
712×	`log1p-expm1-u_binary64`
712×	`expm1-log1p-u_binary64`
698×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	177	8
2	1997	8

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

Inputs
(*.f64 3/8 (/.f64 4 x))
(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 3/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 3/8 (*.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 3/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -3/2 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 3/2 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 3/2 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 3/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 3/2 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 3/2 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 3/2 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 9/4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 3/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 3/2 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 3/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 3/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 3/2 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 2/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2/3 x)) (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2) (cbrt.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8/3 (*.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/4) 8/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2/3 x)) (sqrt.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 3/2 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 3/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 3/2 x)) -1) (pow.f64 (sqrt.f64 (/.f64 3/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 3/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 3/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 3/2 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (/.f64 4 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x 1/4) 3/8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2/3 x)) (sqrt.f64 (/.f64 3/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 3/2 x)) 2)) (cbrt.f64 (/.f64 3/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 3/2 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2/3 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2/3 x)))))))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	96
1	7	96

Stop Event

1×

saturated

Counts

65 → 42

Calls

Call 1

Inputs
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)

Outputs
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(/.f64 3/2 x)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)
(*.f64 2/3 x)
(*.f64 x 2/3)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(/.f64 8/3 (sin.f64 x))
✓	0.4b	(*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
✓	2.6b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 37 to 22 computations (40.5% saved)

series3.0ms (0%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
1.0ms	x	@	inf	(*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
0.0ms	x	@	0	(-.f64 1 (cos.f64 x))
0.0ms	x	@	0	(*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
0.0ms	x	@	-inf	(-.f64 1 (cos.f64 x))

rewrite66.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

977×	`pow1_binary64`
912×	`add-log-exp_binary64`
912×	`log1p-expm1-u_binary64`
912×	`expm1-log1p-u_binary64`
96×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	191	20
2	2421	20

Stop Event

1×	node limit

Counts

2 → 71

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))
(*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x)))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 8/3 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 8/3 (sin.f64 x)) (*.f64 (/.f64 8/3 (sin.f64 x)) (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (cos.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (*.f64 (*.f64 (sin.f64 x) 3/8) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (*.f64 (sin.f64 x) 3/8) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3)) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 1) (*.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (*.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) 1) (*.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) 8/3) (*.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) 8/3) (*.f64 (+.f64 1 (cos.f64 x)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) -8/3) (*.f64 (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) -8/3) (*.f64 (+.f64 1 (cos.f64 x)) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 8/3 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (*.f64 (sin.f64 x) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -8/3 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (*.f64 (neg.f64 (sin.f64 x)) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 8/3 (pow.f64 (sin.f64 x) 2)) (*.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -8/3 (pow.f64 (sin.f64 x) 2)) (*.f64 (neg.f64 (sin.f64 x)) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) 1) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 8/3 (sin.f64 x))) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 8/3 (sin.f64 x))) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -8/3 (-.f64 1 (cos.f64 x))) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (cos.f64 x)) -8/3) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (pow.f64 (cos.f64 x) 3))) (+.f64 1 (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (pow.f64 (sin.f64 x) 2)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (/.f64 8/3 (sin.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3) (pow.f64 (-.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1 (cos.f64 x)) (/.f64 8/3 (sin.f64 x)))))))))

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

750×	`distribute-lft-out_binary64`
698×	`distribute-rgt-out_binary64`
641×	`fma-def_binary64`
619×	`associate-l_binary64`
477×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	200
1	118	200
2	273	200
3	842	200
4	3737	200
5	6159	200
6	6951	200
7	7568	200

Stop Event

1×	node limit

Counts

87 → 89

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(*.f64 4/3 x)
(+.f64 (.f64 4/3 x) (.f64 1/9 (pow.f64 x 3)))
(+.f64 (.f64 1/90 (pow.f64 x 5)) (+.f64 (.f64 4/3 x) (*.f64 1/9 (pow.f64 x 3))))
(+.f64 (.f64 17/15120 (pow.f64 x 7)) (+.f64 (.f64 1/90 (pow.f64 x 5)) (+.f64 (.f64 4/3 x) (.f64 1/9 (pow.f64 x 3)))))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/24 (pow.f64 x 4))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/40320 (pow.f64 x 8) (.f64 1/2 (.f64 x x)))))
(*.f64 4/3 x)
(*.f64 x 4/3)
(+.f64 (.f64 4/3 x) (.f64 1/9 (pow.f64 x 3)))
(fma.f64 4/3 x (*.f64 1/9 (pow.f64 x 3)))
(fma.f64 x 4/3 (*.f64 1/9 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/9) 4/3))
(+.f64 (.f64 1/90 (pow.f64 x 5)) (+.f64 (.f64 4/3 x) (*.f64 1/9 (pow.f64 x 3))))
(fma.f64 1/90 (pow.f64 x 5) (fma.f64 4/3 x (*.f64 1/9 (pow.f64 x 3))))
(fma.f64 1/90 (pow.f64 x 5) (fma.f64 x 4/3 (*.f64 1/9 (pow.f64 x 3))))
(fma.f64 1/9 (pow.f64 x 3) (fma.f64 x 4/3 (*.f64 1/90 (pow.f64 x 5))))
(fma.f64 x 4/3 (fma.f64 1/9 (pow.f64 x 3) (*.f64 1/90 (pow.f64 x 5))))
(+.f64 (.f64 17/15120 (pow.f64 x 7)) (+.f64 (.f64 1/90 (pow.f64 x 5)) (+.f64 (.f64 4/3 x) (.f64 1/9 (pow.f64 x 3)))))
(fma.f64 17/15120 (pow.f64 x 7) (fma.f64 1/90 (pow.f64 x 5) (fma.f64 4/3 x (*.f64 1/9 (pow.f64 x 3)))))
(fma.f64 17/15120 (pow.f64 x 7) (fma.f64 1/90 (pow.f64 x 5) (fma.f64 x 4/3 (*.f64 1/9 (pow.f64 x 3)))))
(fma.f64 17/15120 (pow.f64 x 7) (fma.f64 1/9 (pow.f64 x 3) (fma.f64 x 4/3 (*.f64 1/90 (pow.f64 x 5)))))
(fma.f64 x 4/3 (fma.f64 1/9 (pow.f64 x 3) (fma.f64 17/15120 (pow.f64 x 7) (*.f64 1/90 (pow.f64 x 5)))))
(fma.f64 x (fma.f64 x (.f64 x 1/9) 4/3) (fma.f64 1/90 (pow.f64 x 5) (.f64 17/15120 (pow.f64 x 7))))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))
(*.f64 8/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 8/3 (tan.f64 (/.f64 x 2)))

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
✓	0.4b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
✓	10.9b	(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))

Compiler

Compiled 40 to 29 computations (27.5% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
0.0ms	x	@	inf	(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
0.0ms	x	@	0	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
0.0ms	x	@	inf	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
0.0ms	x	@	0	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))

rewrite75.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

498×	`log-prod_binary64`
390×	`exp-prod_binary64`
276×	`pow2_binary64`
270×	`prod-exp_binary64`
247×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	231	40
2	2665	40

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

Inputs
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) (cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 4)) (cbrt.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) (/.f64 1 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sin.f64 x)) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) 1) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4) 1) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (sin.f64 (*.f64 x 1/2)) (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) -2) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) -1/2) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4) (sqrt.f64 (sin.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) (pow.f64 (sin.f64 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 2)) (cbrt.f64 (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))) (sqrt.f64 (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) (pow.f64 (sin.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1) (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1) (neg.f64 (log.f64 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (neg.f64 (log.f64 (sin.f64 x))) (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sin.f64 x) (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3)) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3) 1) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3) (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) 8/3) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 8/3 (neg.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 4) 64/9) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (sqrt.f64 8/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))) 2)) (cbrt.f64 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)))) (sqrt.f64 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 4) 64/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8/3) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (sqrt.f64 8/3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 8/3)) (*.f64 (log.f64 (sin.f64 x)) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (pow.f64 (sin.f64 (*.f64 x 1/2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3/2) (sqrt.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 5) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (cos.f64 (-.f64 (*.f64 x 1/2) (*.f64 x 1/2))) (cos.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 1) (log.f64 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 1) (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 1)))))))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
753×	`distribute-lft-out_binary64`
717×	`associate-l_binary64`
713×	`distribute-rgt-out_binary64`
569×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	506
1	144	506
2	349	506
3	1068	506
4	4390	506
5	6940	506

Stop Event

1×	node limit

Counts

152 → 145

Calls

Call 1

Inputs
(*.f64 1/4 x)
(+.f64 (.f64 1/48 (pow.f64 x 3)) (.f64 1/4 x))
(+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (*.f64 1/4 x)))
(+.f64 (.f64 17/80640 (pow.f64 x 7)) (+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (.f64 1/4 x))))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)

Outputs
(*.f64 1/4 x)
(+.f64 (.f64 1/48 (pow.f64 x 3)) (.f64 1/4 x))
(fma.f64 1/48 (pow.f64 x 3) (*.f64 1/4 x))
(fma.f64 1/4 x (*.f64 1/48 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/48) 1/4))
(+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (*.f64 1/4 x)))
(fma.f64 1/48 (pow.f64 x 3) (fma.f64 1/480 (pow.f64 x 5) (*.f64 1/4 x)))
(fma.f64 1/4 x (fma.f64 1/480 (pow.f64 x 5) (*.f64 1/48 (pow.f64 x 3))))
(fma.f64 x (fma.f64 x (.f64 x 1/48) 1/4) (.f64 1/480 (pow.f64 x 5)))
(+.f64 (.f64 17/80640 (pow.f64 x 7)) (+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (.f64 1/4 x))))
(fma.f64 17/80640 (pow.f64 x 7) (fma.f64 1/48 (pow.f64 x 3) (fma.f64 1/480 (pow.f64 x 5) (*.f64 1/4 x))))
(fma.f64 17/80640 (pow.f64 x 7) (fma.f64 1/4 x (fma.f64 1/480 (pow.f64 x 5) (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 1/480 (pow.f64 x 5) (fma.f64 17/80640 (pow.f64 x 7) (fma.f64 1/4 x (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 1/480 (pow.f64 x 5) (fma.f64 17/80640 (pow.f64 x 7) (.f64 x (fma.f64 x (.f64 x 1/48) 1/4))))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))
(*.f64 2/3 x)
(*.f64 x 2/3)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 x 2/3))
(fma.f64 (pow.f64 x 3) 1/18 (*.f64 x 2/3))
(fma.f64 x 2/3 (*.f64 (pow.f64 x 3) 1/18))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 (pow.f64 x 5) 1/180)))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 5) 1/180 (*.f64 x 2/3)))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 3) 1/18 (*.f64 (pow.f64 x 5) 1/180)))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (.f64 (pow.f64 x 5) 1/180))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 (pow.f64 x 5) 1/180))))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 7) 17/30240 (fma.f64 (pow.f64 x 5) 1/180 (*.f64 x 2/3))))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 5) 1/180 (fma.f64 (pow.f64 x 7) 17/30240 (*.f64 x 2/3))))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 5) 1/180 (fma.f64 (pow.f64 x 3) 1/18 (*.f64 (pow.f64 x 7) 17/30240))))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 5) 1/180 (*.f64 (pow.f64 x 7) 17/30240))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)) 8/3)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(*.f64 1/4 (pow.f64 x 2))
(.f64 1/4 (.f64 x x))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 1/4 (.f64 x x) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 x (.f64 1/4 x) (.f64 -1/48 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/48 1/4)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/48 1/4) (*.f64 1/1440 (pow.f64 x 6)))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (fma.f64 -1/48 (pow.f64 x 4) (.f64 -1/80640 (pow.f64 x 8)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)

eval199.0ms (2.5%)

Compiler: Compiled 8560 to 6289 computations (26.5% saved)

prune95.0ms (1.2%)

Pruning

25 alts after pruning (17 fresh and 8 done)

	Pruned	Kept	Total
New	540	9	549
Fresh	9	8	17
Picked	0	1	1
Done	1	7	8
Total	550	25	575

Error

Counts

575 → 25

Alt Table

Click to see full alt table

Status	Error	Program
✓	25.7b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
	25.6b	(/.f64 (/.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (sin.f64 x)) 2)
	36.2b	(/.f64 (*.f64 x 1/4) 3/8)
▶	49.2b	(fabs.f64 (*.f64 2/3 x))
	36.5b	(/.f64 8/3 (/.f64 4 x))
	11.3b	(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 (sin.f64 x) 3/8) (+.f64 1 (cos.f64 x)))) 2)
	25.6b	(/.f64 (/.f64 1 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (cos.f64 x)) 8/3))) 2)
	11.2b	(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
▶	0.4b	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
✓	11.1b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
	0.5b	(.f64 (.f64 8/3 (/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))) (sin.f64 (.f64 x 1/2)))
▶	25.7b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
✓	25.6b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
	25.6b	(/.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 3/8)
	25.7b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) 2)
✓	60.5b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
✓	25.7b	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
	36.8b	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
✓	36.3b	(*.f64 2/3 x)
✓	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
▶	11.2b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
▶	36.3b	(/.f64 1 (/.f64 3/2 x))
	25.6b	(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/8)) 2)
	60.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
✓	0.5b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))

Compiler

Compiled 484 to 400 computations (17.4% saved)

localize18.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
1.0ms	x	@	-inf	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
1.0ms	x	@	0	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)

rewrite52.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`pow1_binary64`
634×	`add-log-exp_binary64`
634×	`log1p-expm1-u_binary64`
634×	`expm1-log1p-u_binary64`
624×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	151	9
2	1718	9

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4/3 (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 16/9 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 4/3) (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)))))))

simplify160.0ms (2%)

Algorithm

1×	egg-herbie

Rules

675×	`sqr-pow_binary64`
672×	`cube-prod_binary64`
624×	`unswap-sqr_binary64`
624×	`fabs-mul_binary64`
439×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	194
1	67	194
2	144	194
3	359	194
4	640	194
5	1377	194
6	1999	194
7	2948	194
8	3101	194
9	3347	194
10	3662	194
11	4143	194
12	4822	194
13	5716	194
14	6362	194
15	6873	194
16	7274	194
17	7659	194
18	7871	194

Stop Event

1×	node limit

Counts

25 → 22

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (.f64 1/180 (pow.f64 x 5)))
(fma.f64 x (fma.f64 1/18 (.f64 x x) 2/3) (.f64 1/180 (pow.f64 x 5)))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 2/3 x))))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (fma.f64 1/18 (pow.f64 x 3) (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 1/18 (.f64 x x) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(fma.f64 1/180 (pow.f64 x 5) (fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (.f64 17/30240 (pow.f64 x 7))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 3/2 x))

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 1 (/.f64 3/2 x))
0.0ms	x	@	-inf	(/.f64 1 (/.f64 3/2 x))
0.0ms	x	@	inf	(/.f64 1 (/.f64 3/2 x))

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
520×	`add-log-exp_binary64`
520×	`log1p-expm1-u_binary64`
520×	`expm1-log1p-u_binary64`
510×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	129	4
2	1501	4

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(/.f64 1 (/.f64 3/2 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 2/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 2/3)) (pow.f64 (cbrt.f64 (*.f64 x 2/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x 2/3)) 2) (cbrt.f64 (*.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 2/3)) (sqrt.f64 (*.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -3/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2/3 (pow.f64 (/.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 3/2 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 3/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 3/2 x)) -1) (pow.f64 (sqrt.f64 (/.f64 3/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2/3 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2/3 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 3/2 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 2/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 2/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 2/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 4/9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 2/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 2/3)))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

38 → 26

Calls

Call 1

Inputs
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)

Outputs
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)
(*.f64 2/3 x)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.3b	(*.f64 2/3 x)

Compiler

Compiled 10 to 7 computations (30% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x))))
	0.4b	(/.f64 8/3 (sin.f64 x))
✓	0.4b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	2.6b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 44 to 29 computations (34.1% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
1.0ms	x	@	inf	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
1.0ms	x	@	-inf	(/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x))))
1.0ms	x	@	inf	(/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x))))
0.0ms	x	@	0	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

603×	`log-prod_binary64`
325×	`pow2_binary64`
228×	`pow1/3_binary64`
226×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	271	26
2	3561	26

Stop Event

1×	node limit

Counts

2 → 100

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
(/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (*.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (*.f64 (sin.f64 x) 3/8) (/.f64 2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sin.f64 x)) 8/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sin.f64 x) (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (*.f64 (sin.f64 x) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (*.f64 (/.f64 -2 (-.f64 1 (cos.f64 x))) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (*.f64 (neg.f64 (sin.f64 x)) (/.f64 -2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 8/3 (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 8/3 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (/.f64 64/9 (pow.f64 (sin.f64 x) 2))) (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (cbrt.f64 (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 8/3 (sin.f64 x))) (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (/.f64 -2 (-.f64 1 (cos.f64 x))) (*.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (*.f64 (sin.f64 x) 3/8) (/.f64 -2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -8/3 (neg.f64 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -8/3 (*.f64 (/.f64 -2 (-.f64 1 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -8/3 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -8/3 (*.f64 (neg.f64 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -8/3 (*.f64 (sin.f64 x) (/.f64 -2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 8/3) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 8/3 (sin.f64 x))) (/.f64 -2 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 8/3)) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 8/3 (sin.f64 x)) (sqrt.f64 (/.f64 2 (-.f64 1 (cos.f64 x))))) (sqrt.f64 (/.f64 2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 8/3 (sin.f64 x)) 1) (/.f64 2 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 8/3 (sin.f64 x)) 2) (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 8/3 (sin.f64 x)) (pow.f64 (cbrt.f64 (/.f64 2 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (/.f64 2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 8/3) 1) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 8/3) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 8/3) (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (/.f64 8/3 (sin.f64 x))) (/.f64 -2 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -8/3 (-.f64 1/2 (/.f64 (cos.f64 x) 2))) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) -8/3) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) -1) (/.f64 -2 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3) (pow.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 3) (pow.f64 (/.f64 8/3 (sin.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3) (pow.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (*.f64 (sin.f64 x) 3/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (sin.f64 x) 3/8) (/.f64 2 (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sin.f64 x)) 8/3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (/.f64 8/3 (sin.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 8/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3) (pow.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 3) (pow.f64 (/.f64 8/3 (sin.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3) (pow.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) (/.f64 8/3 (sin.f64 x)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1/2 (/.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 (neg.f64 (cos.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 1/2 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (/.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1/2 (/.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (cos.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))) (cbrt.f64 (*.f64 1/4 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 (-.f64 1 (cos.f64 x)) 2))) (cbrt.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))) (sqrt.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -2 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 2 (-.f64 1 (cos.f64 x)))) -2) (cbrt.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/4 (pow.f64 (-.f64 1 (cos.f64 x)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 2 (-.f64 1 (cos.f64 x)))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 (-.f64 1 (cos.f64 x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (/.f64 -2 (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 (-.f64 1 (cos.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 2 (-.f64 1 (cos.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 1/2 (/.f64 (cos.f64 x) 2))) 1))))))

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

747×	`distribute-lft-out_binary64`
701×	`distribute-rgt-out_binary64`
627×	`fma-def_binary64`
618×	`associate-l_binary64`
489×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	272
1	123	272
2	288	272
3	859	256
4	3776	256
5	6210	256
6	7019	256
7	7650	256

Stop Event

1×	node limit

Counts

124 → 118

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 3))))
(fma.f64 x (fma.f64 1/18 (.f64 x x) 2/3) (.f64 1/180 (pow.f64 x 5)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (fma.f64 1/18 (pow.f64 x 3) (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 1/18 (.f64 x x) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 1/4 (pow.f64 x 2))
(.f64 1/4 (.f64 x x))
(.f64 x (.f64 x 1/4))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 1/4 (.f64 x x) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 x (.f64 x 1/4) (.f64 -1/48 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/48) 1/4))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/48) 1/4)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 x (.f64 x 1/4) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/48) 1/4) (*.f64 1/1440 (pow.f64 x 6)))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 x (.f64 x 1/4) (fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 x (.f64 x 1/4) (fma.f64 1/1440 (pow.f64 x 6) (fma.f64 -1/80640 (pow.f64 x 8) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 x (.f64 x 1/4) (fma.f64 1/1440 (pow.f64 x 6) (fma.f64 -1/48 (pow.f64 x 4) (.f64 -1/80640 (pow.f64 x 8)))))
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)
(*.f64 1/2 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1/2)
(fma.f64 -1/2 (cos.f64 x) 1/2)
(fma.f64 (cos.f64 x) -1/2 1/2)

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
✓	0.3b	(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
✓	10.9b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))

Compiler

Compiled 39 to 30 computations (23.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
0.0ms	x	@	inf	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
0.0ms	x	@	-inf	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
0.0ms	x	@	0	(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
0.0ms	x	@	inf	(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))

rewrite72.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
409×	`exp-prod_binary64`
277×	`pow2_binary64`
252×	`pow-prod-down_binary64`
194×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	231	29
2	2734	29

Stop Event

1×	node limit

Counts

2 → 84

Calls

Call 1

Inputs
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8/3 (/.f64 1 (*.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8/3 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (*.f64 8/3 (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) (cbrt.f64 (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9) (pow.f64 (sin.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9) (pow.f64 (sin.f64 x) -2))) (cbrt.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9)) (*.f64 (cbrt.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 (sin.f64 x))) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (/.f64 1 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) -8/3) (/.f64 1 (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sin.f64 x)) (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 1) (/.f64 8/3 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9)) 1) (/.f64 (cbrt.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) 1) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8/3 (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 8/3 (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) -2) (/.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (cbrt.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (cbrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 8/3 (sqrt.f64 (sin.f64 x))) (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sqrt.f64 (sin.f64 x))) (/.f64 8/3 (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 x) -1/2) (/.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9)) (sqrt.f64 (sin.f64 x))) (/.f64 (cbrt.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) (sqrt.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9) (pow.f64 (sin.f64 x) -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 (sin.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 3/8 (*.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 8/3 (/.f64 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sqrt.f64 (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9) (pow.f64 (sin.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 8/3 (sin.f64 x))) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) 6) (pow.f64 (sin.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 (sin.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 3/8 (*.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 8/3 (/.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (sin.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1) (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) (*.f64 (log.f64 (sin.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 2)) (cbrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (sqrt.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 64/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1) 1))))))

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

732×	`distribute-lft-out_binary64`
706×	`distribute-rgt-out_binary64`
616×	`associate-l_binary64`
598×	`fma-def_binary64`
495×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	360
1	123	360
2	283	360
3	851	360
4	3682	360
5	6192	360
6	7424	360

Stop Event

1×	node limit

Counts

108 → 103

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(*.f64 2/3 (pow.f64 x 2))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (.f64 2/3 (pow.f64 x 2)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (*.f64 1/540 (pow.f64 x 6))))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (+.f64 (.f64 -1/30240 (pow.f64 x 8)) (.f64 1/540 (pow.f64 x 6)))))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 3))))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 2/3 x (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (.f64 x (fma.f64 1/18 (.f64 x x) 2/3))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(*.f64 2/3 (pow.f64 x 2))
(.f64 2/3 (.f64 x x))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (.f64 2/3 (pow.f64 x 2)))
(fma.f64 -1/18 (pow.f64 x 4) (.f64 2/3 (.f64 x x)))
(fma.f64 2/3 (.f64 x x) (.f64 -1/18 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/18) 2/3))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/18) 2/3)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (*.f64 1/540 (pow.f64 x 6))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (.f64 1/540 (pow.f64 x 6))))
(fma.f64 2/3 (.f64 x x) (fma.f64 -1/18 (pow.f64 x 4) (.f64 1/540 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/18) 2/3) (*.f64 1/540 (pow.f64 x 6)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (+.f64 (.f64 -1/30240 (pow.f64 x 8)) (.f64 1/540 (pow.f64 x 6)))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (fma.f64 -1/30240 (pow.f64 x 8) (.f64 1/540 (pow.f64 x 6)))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (fma.f64 1/540 (pow.f64 x 6) (.f64 -1/30240 (pow.f64 x 8)))))
(fma.f64 2/3 (.f64 x x) (fma.f64 -1/18 (pow.f64 x 4) (fma.f64 1/540 (pow.f64 x 6) (.f64 -1/30240 (pow.f64 x 8)))))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))

eval146.0ms (1.8%)

Compiler: Compiled 6079 to 4405 computations (27.5% saved)

prune69.0ms (0.9%)

Pruning

24 alts after pruning (17 fresh and 7 done)

	Pruned	Kept	Total
New	398	10	408
Fresh	5	7	12
Picked	0	1	1
Done	6	6	12
Total	409	24	433

Error

Counts

433 → 24

Alt Table

Click to see full alt table

Status	Error	Program
	25.7b	(/.f64 (/.f64 8/3 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x))))
	0.4b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))
	36.2b	(/.f64 (*.f64 x 1/4) 3/8)
	25.7b	(/.f64 8/3 (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
✓	49.2b	(fabs.f64 (*.f64 2/3 x))
	24.9b	(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
	25.6b	(/.f64 (/.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (sin.f64 x)) 2)
	36.5b	(/.f64 8/3 (/.f64 4 x))
	0.4b	(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
	1.1b	(log1p.f64 (expm1.f64 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)))
	25.6b	(/.f64 (/.f64 1 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (cos.f64 x)) 8/3))) 2)
	25.7b	(/.f64 1 (/.f64 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sin.f64 x)) 8/3))
	11.4b	(.f64 8/3 (/.f64 1 (.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2))))
✓	25.7b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
✓	60.5b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
	36.8b	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
	42.0b	(pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) 4/3) 3) 1/3)
✓	36.3b	(*.f64 2/3 x)
✓	11.2b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
✓	36.3b	(/.f64 1 (/.f64 3/2 x))
	25.6b	(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/8)) 2)
✓	0.4b	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
	25.7b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
	60.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))

Compiler

Compiled 256 to 216 computations (15.6% saved)

regimes91.0ms (1.1%)

Counts

65 → 1

Calls

Call 1

Inputs
(*.f64 2/3 x)
(/.f64 (*.f64 x 1/4) 3/8)
(/.f64 8/3 (/.f64 4 x))
(/.f64 1 (/.f64 3/2 x))
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
(fabs.f64 (*.f64 2/3 x))
(pow.f64 (/.f64 3/2 x) -1)
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
(pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)
(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(/.f64 (/.f64 8/3 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x))))
(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(/.f64 (/.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (sin.f64 x)) 2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/8)) 2)
(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
(/.f64 8/3 (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(/.f64 1 (/.f64 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sin.f64 x)) 8/3))
(/.f64 (/.f64 1 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (cos.f64 x)) 8/3))) 2)
(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
(+.f64 0 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))
(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(log1p.f64 (expm1.f64 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)))
(pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) 4/3) 3) 1/3)
(/.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 3/8)
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 1 (.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2))))
(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))
(.f64 (.f64 8/3 (/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))) (sin.f64 (.f64 x 1/2)))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (*.f64 (/.f64 1 (sin.f64 x)) 8/3))
(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) 2)
(/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 2) (sin.f64 x))
(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6)) (/.f64 8/3 (sin.f64 x)))
(pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
(log1p.f64 (expm1.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))
(/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))))) 1) (sin.f64 x))
(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 (sin.f64 x) 3/8) (+.f64 1 (cos.f64 x)))) 2)
(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
(/.f64 (pow.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 6) 1/3) (sin.f64 x))
(.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
(.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 1) (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))))
(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 x))))
(.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))

Outputs
(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))

Calls

2 calls:

35.0ms	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
32.0ms	x

Results

Error	Segments	Branch
0.3b	1	`x`
0.3b	1	`(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))`

Compiler

Compiled 780 to 565 computations (27.6% saved)

regimes36.0ms (0.5%)

Counts

44 → 1

Calls

Call 1

Inputs
(*.f64 2/3 x)
(/.f64 (*.f64 x 1/4) 3/8)
(/.f64 8/3 (/.f64 4 x))
(/.f64 1 (/.f64 3/2 x))
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
(fabs.f64 (*.f64 2/3 x))
(pow.f64 (/.f64 3/2 x) -1)
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
(pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)
(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(/.f64 (/.f64 8/3 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x))))
(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(/.f64 (/.f64 (*.f64 (-.f64 1 (cos.f64 x)) 8/3) (sin.f64 x)) 2)
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/8)) 2)
(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
(/.f64 8/3 (/.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(/.f64 1 (/.f64 (*.f64 (/.f64 2 (-.f64 1 (cos.f64 x))) (sin.f64 x)) 8/3))
(/.f64 (/.f64 1 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (cos.f64 x)) 8/3))) 2)
(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
(+.f64 0 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))
(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(log1p.f64 (expm1.f64 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)))
(pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) 4/3) 3) 1/3)
(/.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 3/8)
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 1 (.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2))))
(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)

Outputs
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))

Calls

1 calls:

22.0ms

Results

Error	Segments	Branch
0.4b	1	`x`

Compiler

Compiled 436 to 315 computations (27.8% saved)

regimes18.0ms (0.2%)

Counts

21 → 1

Calls

Call 1

Inputs
(*.f64 2/3 x)
(/.f64 (*.f64 x 1/4) 3/8)
(/.f64 8/3 (/.f64 4 x))
(/.f64 1 (/.f64 3/2 x))
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
(fabs.f64 (*.f64 2/3 x))
(pow.f64 (/.f64 3/2 x) -1)
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(pow.f64 (*.f64 3/8 (/.f64 4 x)) -1)
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
(pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)
(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(/.f64 (/.f64 8/3 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x))))
(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))

Outputs
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
0.4b	1	`x`

Compiler

Compiled 166 to 124 computations (25.3% saved)

regimes8.0ms (0.1%)

Accuracy

Total -25.5b remaining (-70.4%)

Threshold costs -25.5b (-70.4%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 2/3 x)
(/.f64 (*.f64 x 1/4) 3/8)
(/.f64 8/3 (/.f64 4 x))
(/.f64 1 (/.f64 3/2 x))
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
(fabs.f64 (*.f64 2/3 x))
(pow.f64 (/.f64 3/2 x) -1)

Outputs
(/.f64 (*.f64 x 1/4) 3/8)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
36.2b	1	`x`

Compiler

Compiled 58 to 47 computations (19% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	59
1	29	59

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(/.f64 (*.f64 x 1/4) 3/8)
(*.f64 2/3 x)

Outputs
(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
(.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2))))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(/.f64 (*.f64 x 1/4) 3/8)
(*.f64 2/3 x)
(*.f64 x 2/3)

Compiler

Compiled 44 to 36 computations (18.2% saved)

soundness0.0ms (0%)

end42.0ms (0.5%)

Compiler: Compiled 40 to 32 computations (20% saved)