Details

analyze849.0ms (10.1%)

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)

sample3.1s (37%)

Results

1.3s	2060×	body	1024	valid
1.3s	5179×	body	256	valid
462.0ms	1009×	body	512	valid
9.0ms	8×	body	2048	valid

preprocess26.0ms (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)))

eval1.0ms (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

16.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.2b	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
▶	16.3b	(.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)

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))
✓	0.3b	(/.f64 8/3 (sin.f64 x))
✓	16.1b	(.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)

series7.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

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

rewrite80.0ms (1%)

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))))))

simplify67.0ms (0.8%)

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)

localize30.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.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)))
✓	16.0b	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))

New

Error

Program

✓

0.2b

(*.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)))

✓

16.0b

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

rewrite82.0ms (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))))))

simplify69.0ms (0.8%)

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))

eval169.0ms (2%)

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

prune85.0ms (1%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	229	36	265
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	231	36	267

Error

0.0b

Counts

267 → 36

Alt Table

Click to see full alt table

Status	Error	Program
	16.3b	(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
	16.3b	(/.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))))
	30.0b	(/.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)))
	25.7b	(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6)) (/.f64 8/3 (sin.f64 x)))
	29.7b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	44.9b	(pow.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 6) (pow.f64 (sin.f64 x) 3)) 1/3)
	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))))
	30.0b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x)))))) (/.f64 8/3 (sin.f64 x)))
	32.8b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
	31.4b	(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)))
	48.1b	(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
	31.4b	(pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)
	29.7b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
	32.7b	(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
	0.6b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
	48.1b	(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
▶	29.7b	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
	16.2b	(/.f64 (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
	17.3b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 3) (/.f64 8/3 (sin.f64 x)))
	16.3b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
▶	32.1b	(*.f64 2/3 x)
▶	40.1b	(expm1.f64 (log1p.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))
▶	0.5b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
	29.7b	(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
	17.3b	(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 6) (/.f64 8/3 (sin.f64 x)))
	29.6b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
	29.7b	(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))
	29.7b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
	47.8b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (+.f64 (.f64 4/9 x) (.f64 8/3 (/.f64 1 x))))
	16.2b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
	29.7b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
	29.7b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
	31.3b	(.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))))
▶	16.2b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))

Compiler

Compiled 1046 to 852 computations (18.5% saved)

localize23.0ms (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)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite85.0ms (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

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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)))))))

simplify81.0ms (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
✓	0.4b	(*.f64 2/3 x)

Compiler

Compiled 6 to 4 computations (33.3% saved)

series3.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite46.0ms (0.5%)

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))))))

simplify9.0ms (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

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sin.f64 x))
✓	0.2b	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
✓	0.2b	(.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x)))
✓	1.9b	(-.f64 1/2 (*.f64 1/2 (cos.f64 x)))

Compiler

Compiled 47 to 30 computations (36.2% saved)

series7.0ms (0.1%)

Counts

4 → 32

Calls

12 calls:

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

rewrite93.0ms (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 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x)))
(.f64 8/3 (.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 (cbrt.f64 (.f64 1/4 (pow.f64 (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 (cbrt.f64 (.f64 1/4 (pow.f64 (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 (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 (sin.f64 x)) (/.f64 (.f64 1/2 (cos.f64 x)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))))) (#(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 (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 (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) (/.f64 (sin.f64 x) (sqrt.f64 (fma.f64 (cos.f64 x) -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3))) (.f64 (sin.f64 x) (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 (sin.f64 x) (fma.f64 1/2 (cos.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (cos.f64 x) -1/2 1/2)) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3))) 1) (.f64 (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2))) 1) (.f64 (fma.f64 1/2 (cos.f64 x) 1/2) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3))) -1) (.f64 (fma.f64 (.f64 1/2 (cos.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2) 1/4) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2))) -1) (.f64 (fma.f64 1/2 (cos.f64 x) 1/2) (neg.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3)))) (.f64 (neg.f64 (sin.f64 x)) (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 (-.f64 1/4 (.f64 1/4 (pow.f64 (cos.f64 x) 2)))) (.f64 (neg.f64 (sin.f64 x)) (fma.f64 1/2 (cos.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) 1) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/8 (.f64 1/8 (pow.f64 (cos.f64 x) 3))) (/.f64 1 (sin.f64 x))) (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))) (/.f64 1 (sin.f64 x))) (fma.f64 1/2 (cos.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (fma.f64 (cos.f64 x) -1/2 1/2)) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 (cos.f64 x) -1/2 1/2) -1) (neg.f64 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 1 (sin.f64 x)) (-.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 (/.f64 1 (sin.f64 x)) (-.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 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 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.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 (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 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x))) 2)))) (#(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 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (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 (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 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3))) 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 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 64/9 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 64/9 (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 (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 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (fma.f64 (cos.f64 x) -1/2 1/2) (sin.f64 x)) 8/3))) 2))))))
((#(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 (cbrt.f64 (/.f64 1 (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)) (cbrt.f64 (/.f64 1 (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) (cbrt.f64 (/.f64 1 (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 (cbrt.f64 (/.f64 1 (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))))))

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

826×	`distribute-rgt-out_binary64`
756×	`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	1360	443
4	3225	443
5	6140	379
6	7559	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 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 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 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 1/4 (.f64 x x) (.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 1/4 (.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 1/4 (.f64 x x) (.f64 1/1440 (pow.f64 x 6)))))
(*.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 (.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 1/48 (pow.f64 x 3) (fma.f64 1/4 x (*.f64 1/480 (pow.f64 x 5))))
(fma.f64 1/4 x (fma.f64 1/48 (pow.f64 x 3) (*.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 1/48 (pow.f64 x 3) (fma.f64 17/80640 (pow.f64 x 7) (fma.f64 1/4 x (*.f64 1/480 (pow.f64 x 5)))))
(/.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 (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 -1/2 (cos.f64 x))) (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 -1/2 (cos.f64 x))) (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 -1/2 (cos.f64 x))) (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 -1/2 (cos.f64 x))) (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 -1/2 (cos.f64 x))) (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 -1/2 (cos.f64 x))) (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 -1/2 (cos.f64 x))) (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 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 (.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)))
(+.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 7) 17/30240 (fma.f64 (pow.f64 x 3) 1/18 (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))))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(.f64 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (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 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (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 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (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 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (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 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (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 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (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 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (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 (/.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(.f64 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)) 8/3)
(/.f64 (+.f64 4/3 (*.f64 (cos.f64 x) -4/3)) (sin.f64 x))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(/.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)))
(+.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 x 1/6 (fma.f64 (pow.f64 x 3) 7/360 (fma.f64 (pow.f64 x 5) 31/15120 (/.f64 1 x))))

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
✓	0.3b	(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
✓	16.0b	(/.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)

series3.0ms (0%)

Counts

3 → 36

Calls

9 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	@	0	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)

rewrite79.0ms (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	38
1	231	38
2	2734	38

Stop Event

1×	node limit

Counts

3 → 110

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

((#(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 (cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4)) (cbrt.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))) (cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4)))))) (#(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))))))

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-def_binary64`
706×	`associate-*l/_binary64`
556×	`distribute-rgt-out_binary64`
542×	`associate-/r*_binary64`
509×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	502
1	151	502
2	359	502
3	1143	502
4	3163	502
5	4243	502
6	5753	502
7	6845	502

Stop Event

1×	node limit

Counts

146 → 139

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))
(*.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 (.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))))
(+.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 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 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(.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 (.f64 x x) (fma.f64 x (.f64 x -1/18) 2/3) (*.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))))
(+.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 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)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/18) 2/3) (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))
(*.f64 1/4 (pow.f64 x 2))
(.f64 (.f64 x x) 1/4)
(.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 (pow.f64 x 4) -1/48))
(fma.f64 (.f64 x x) 1/4 (.f64 (pow.f64 x 4) -1/48))
(fma.f64 x (.f64 x 1/4) (.f64 (pow.f64 x 4) -1/48))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/48) 1/4))
(.f64 (.f64 x 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 (pow.f64 x 4) -1/48)))
(fma.f64 (.f64 x x) 1/4 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440)))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/48) 1/4) (*.f64 (pow.f64 x 6) 1/1440))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 6) 1/1440 (.f64 (pow.f64 x 4) -1/48)))
(+.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 (pow.f64 x 4) -1/48))))
(fma.f64 (pow.f64 x 8) -1/80640 (fma.f64 (.f64 x x) 1/4 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440))))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 8) -1/80640 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440))))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 6) 1/1440 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 8) -1/80640))))
(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 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))
✓	0.2b	(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
✓	0.2b	(/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))
	1.9b	(-.f64 1/2 (*.f64 1/2 (cos.f64 x)))

Compiler

Compiled 63 to 40 computations (36.5% saved)

series4.0ms (0%)

Counts

3 → 28

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
1.0ms	x	@	-inf	(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
0.0ms	x	@	0	(/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
0.0ms	x	@	0	(/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))
0.0ms	x	@	0	(expm1.f64 (log1p.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))

rewrite87.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`log-prod_binary64`
342×	`prod-diff_binary64`
315×	`pow2_binary64`
292×	`pow-prod-down_binary64`
221×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	251	48
2	3278	42

Stop Event

1×	node limit

Counts

3 → 138

Calls

Call 1

Inputs

(/.f64 8/3 (/.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))))

(expm1.f64 (log1p.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))

Outputs

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

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simplify108.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

954×	`fma-def_binary64`
810×	`fma-neg_binary64`
624×	`unswap-sqr_binary64`
471×	`associate-l_binary64`
312×	`associate-r_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	45	437
1	115	437
2	268	389
3	693	357
4	1284	357
5	2627	309
6	3980	309
7	5482	309
8	6438	309
9	7615	309

Stop Event

1×	node limit

Counts

166 → 114

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 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)))))
(*.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)))

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))
(.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 1/180 (pow.f64 x 5) (fma.f64 2/3 x (*.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 x (.f64 x 1/18) 2/3))))
(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))))
(.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 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)))
(+.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 -1/3 (fma.f64 (pow.f64 x 3) -1/180 (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))))
(*.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))
(.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 1/180 (pow.f64 x 5) (fma.f64 2/3 x (*.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 x (.f64 x 1/18) 2/3))))
(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))))
(.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)))

eval357.0ms (4.3%)

Compiler: Compiled 11775 to 8532 computations (27.5% saved)

prune119.0ms (1.4%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	675	16	691
Fresh	23	8	31
Picked	1	0	1
Done	2	2	4
Total	701	26	727

Error

Counts

727 → 26

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.3b	(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
	61.0b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
	32.6b	(expm1.f64 (log1p.f64 (/.f64 8/3 (/.f64 4 x))))
	29.7b	(.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (*.f64 8/3 (/.f64 1 (sin.f64 x))))
	10.8b	(expm1.f64 (log1p.f64 (*.f64 4/3 (tan.f64 (/.f64 x 2)))))
	0.3b	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
▶	60.6b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
	16.3b	(pow.f64 (.f64 3/8 (.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2))) -1)
	52.9b	(cbrt.f64 (*.f64 (pow.f64 x 3) 8/27))
▶	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
	46.2b	(fabs.f64 (*.f64 2/3 x))
	48.1b	(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
	29.7b	(/.f64 1 (*.f64 (/.f64 (sin.f64 x) (fma.f64 (cos.f64 x) -1/2 1/2)) 3/8))
	31.4b	(pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)
	29.7b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
✓	32.1b	(*.f64 2/3 x)
▶	29.6b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
	47.3b	(pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)
	29.7b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
✓	16.2b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
	0.5b	(.f64 (.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))) (sin.f64 (.f64 x 1/2)))
	47.8b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (+.f64 (.f64 4/9 x) (.f64 8/3 (/.f64 1 x))))
	29.7b	(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))
	29.7b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
▶	32.7b	(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
	29.7b	(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 578 to 483 computations (16.4% saved)

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.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)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite89.0ms (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 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))))))

simplify68.0ms (0.8%)

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))))

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 2/3 x))
	0.4b	(*.f64 2/3 x)
✓	2.3b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series5.0ms (0.1%)

Counts

2 → 18

Calls

6 calls:

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

rewrite72.0ms (0.9%)

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	17
1	156	9
2	2109	9

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

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

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)))))

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

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	72
1	11	72
2	12	72

Stop Event

1×

saturated

Counts

97 → 81

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)
1
(+.f64 (*.f64 2/3 x) 1)
(+.f64 (*.f64 2/3 x) 1)
(+.f64 (*.f64 2/3 x) 1)
(*.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)
1
(+.f64 (*.f64 2/3 x) 1)
(fma.f64 2/3 x 1)
(+.f64 (*.f64 2/3 x) 1)
(fma.f64 2/3 x 1)
(+.f64 (*.f64 2/3 x) 1)
(fma.f64 2/3 x 1)
(*.f64 2/3 x)
(*.f64 2/3 x)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(*.f64 2/3 x)
✓	0.6b	(cbrt.f64 (*.f64 2/3 x))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series8.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
2.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 2/3 x))
1.0ms	x	@	0	(cbrt.f64 (*.f64 2/3 x))

rewrite53.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`pow1_binary64`
516×	`add-sqr-sqrt_binary64`
495×	`add-log-exp_binary64`
495×	`log1p-expm1-u_binary64`
495×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	149	10
2	1397	10

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
(cbrt.f64 (*.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 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 1 (*.f64 2/3 x))))) (#(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 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 2/3 x))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 2/3 x))) (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2/3) (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2)))))) (#(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 (pow.f64 (*.f64 2/3 x) 1/6) (*.f64 (pow.f64 (*.f64 2/3 x) 1/6) (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2)))))) (#(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 (cbrt.f64 (*.f64 2/3 x))) 2) 3) (cbrt.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 2/3) 3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 2/3 x) 1/6) 3) (pow.f64 (pow.f64 (*.f64 2/3 x) 1/6) 3))))) (#(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 (*.f64 (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2) 1) (cbrt.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 2/3 x))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 2/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2) (cbrt.f64 2/3)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 2/3 x)) 2) (pow.f64 (*.f64 2/3 x) 1/6)) (pow.f64 (*.f64 2/3 x) 1/6))))) (#(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 (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)))))))

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

49 → 49

Calls

Call 1

Inputs

Outputs

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 x)
✓	0.1b	(*.f64 (sin.f64 x) 3/8)
✓	0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
✓	1.9b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 34 to 21 computations (38.2% saved)

series6.0ms (0.1%)

Counts

4 → 32

Calls

12 calls:

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

rewrite105.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

584×	`log-prod_binary64`
292×	`pow2_binary64`
287×	`pow-prod-down_binary64`
274×	`prod-diff_binary64`
204×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	236	29
2	3117	24

Stop Event

1×	node limit

Counts

4 → 209

Calls

Call 1

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

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

944×	`distribute-lft-out_binary64`
765×	`associate-/l/_binary64`
382×	`unswap-sqr_binary64`
369×	`associate-+l+_binary64`
361×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	358
1	186	356
2	449	354
3	1417	354
4	2249	354
5	4189	354
6	5101	354
7	5804	354
8	7841	354

Stop Event

1×	node limit

Counts

241 → 244

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 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 3/8 x)
(+.f64 (.f64 -1/16 (pow.f64 x 3)) (.f64 3/8 x))
(+.f64 (.f64 1/320 (pow.f64 x 5)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (*.f64 3/8 x)))
(+.f64 (.f64 1/320 (pow.f64 x 5)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (+.f64 (.f64 -1/13440 (pow.f64 x 7)) (.f64 3/8 x))))
(*.f64 3/8 (sin.f64 x))
(*.f64 3/8 (sin.f64 x))
(*.f64 3/8 (sin.f64 x))
(*.f64 3/8 (sin.f64 x))
(*.f64 3/8 (sin.f64 x))
(*.f64 3/8 (sin.f64 x))
(*.f64 3/8 (sin.f64 x))
(*.f64 3/8 (sin.f64 x))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))

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)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.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 -1/24 (pow.f64 x 4) (fma.f64 1/2 (.f64 x x) (.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)))))
(*.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 x 2/3 (fma.f64 17/30240 (pow.f64 x 7) (*.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))))
(*.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 3/8 x)
(*.f64 x 3/8)
(+.f64 (.f64 -1/16 (pow.f64 x 3)) (.f64 3/8 x))
(fma.f64 -1/16 (pow.f64 x 3) (*.f64 x 3/8))
(fma.f64 (pow.f64 x 3) -1/16 (*.f64 x 3/8))
(fma.f64 x 3/8 (*.f64 (pow.f64 x 3) -1/16))
(+.f64 (.f64 1/320 (pow.f64 x 5)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (*.f64 3/8 x)))
(fma.f64 1/320 (pow.f64 x 5) (fma.f64 -1/16 (pow.f64 x 3) (*.f64 x 3/8)))
(fma.f64 (pow.f64 x 5) 1/320 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 x 3/8)))
(fma.f64 (pow.f64 x 3) -1/16 (fma.f64 (pow.f64 x 5) 1/320 (*.f64 x 3/8)))
(fma.f64 x 3/8 (fma.f64 (pow.f64 x 5) 1/320 (*.f64 (pow.f64 x 3) -1/16)))
(fma.f64 x 3/8 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 (pow.f64 x 5) 1/320)))
(+.f64 (.f64 1/320 (pow.f64 x 5)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (+.f64 (.f64 -1/13440 (pow.f64 x 7)) (.f64 3/8 x))))
(fma.f64 1/320 (pow.f64 x 5) (fma.f64 -1/16 (pow.f64 x 3) (fma.f64 -1/13440 (pow.f64 x 7) (*.f64 x 3/8))))
(fma.f64 (pow.f64 x 5) 1/320 (fma.f64 (pow.f64 x 3) -1/16 (fma.f64 (pow.f64 x 7) -1/13440 (*.f64 x 3/8))))
(fma.f64 (pow.f64 x 3) -1/16 (fma.f64 (pow.f64 x 5) 1/320 (fma.f64 (pow.f64 x 7) -1/13440 (*.f64 x 3/8))))
(fma.f64 (pow.f64 x 5) 1/320 (fma.f64 (pow.f64 x 7) -1/13440 (fma.f64 x 3/8 (*.f64 (pow.f64 x 3) -1/16))))
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
(*.f64 3/8 (sin.f64 x))
(*.f64 (sin.f64 x) 3/8)
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 (pow.f64 x 4) 1/24)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 1/24 (.f64 (.f64 x x) -1/2)))
(fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (*.f64 x x) -1/2 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (.f64 (pow.f64 x 6) -1/720))))
(+.f64 (fma.f64 (.f64 x x) -1/2 1) (fma.f64 (pow.f64 x 4) 1/24 (.f64 (pow.f64 x 6) -1/720)))
(+.f64 (fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (.f64 x x) -1/2 1)) (.f64 (pow.f64 x 6) -1/720))
(+.f64 1 (fma.f64 (pow.f64 x 4) 1/24 (fma.f64 x (.f64 x -1/2) (.f64 (pow.f64 x 6) -1/720))))

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
	0.3b	(/.f64 8/3 (sin.f64 x))
✓	16.1b	(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 35 to 25 computations (28.6% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

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

0.0ms

inf

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

0.0ms

-inf

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

rewrite62.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

478×	`log-prod_binary64`
372×	`exp-prod_binary64`
287×	`prod-exp_binary64`
273×	`pow2_binary64`
260×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	232	17
2	2614	17

Stop Event

1×	node limit

Counts

1 → 42

Calls

Call 1

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

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

simplify112.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

866×	`unswap-sqr_binary64`
544×	`associate-*r/_binary64`
486×	`sqr-pow_binary64`
439×	`fma-def_binary64`
394×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	194
1	73	194
2	160	194
3	408	194
4	788	194
5	1984	194
6	3617	194
7	5388	194
8	6301	194
9	6672	194
10	7141	194
11	7870	194

Stop Event

1×	node limit

Counts

54 → 51

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)))

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 2/3 x (fma.f64 1/18 (pow.f64 x 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)))
(+.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 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 1/18 (pow.f64 x 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 1/18 (pow.f64 x 3) (*.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))))
(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 (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)))

eval405.0ms (4.8%)

Compiler: Compiled 13248 to 9532 computations (28% saved)

prune100.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	708	8	716
Fresh	16	3	19
Picked	1	0	1
Done	4	2	6
Total	729	13	742

Error

Counts

742 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	0.3b	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
✓	60.6b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
	20.6b	(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))
▶	29.4b	(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)
▶	0.1b	(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
	29.7b	(-.f64 (/.f64 1/2 (.f64 (sin.f64 x) 3/8)) (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4)))
	29.6b	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
	61.0b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
▶	46.2b	(fabs.f64 (*.f64 2/3 x))
▶	29.6b	(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4)))
✓	32.1b	(*.f64 2/3 x)
	29.7b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
▶	61.3b	(-.f64 1 1)

Compiler

Compiled 236 to 198 computations (16.1% saved)

localize15.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (tan.f64 (/.f64 x 2)) 3/4)

Compiler

Compiled 26 to 21 computations (19.2% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

732×	`pow1_binary64`
690×	`add-log-exp_binary64`
690×	`log1p-expm1-u_binary64`
690×	`expm1-log1p-u_binary64`
680×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	159	9
2	1869	9

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

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

simplify163.0ms (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

35 → 32

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))))

localize2.0ms (0%)

Compiler: Compiled 5 to 5 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 10 to 7 computations (30% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)
0.0ms	x	@	inf	(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)
0.0ms	x	@	-inf	(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)

rewrite51.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`pow1_binary64`
619×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
609×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	148	9
2	1670	9

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify159.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	130
1	65	130
2	136	130
3	339	130
4	622	130
5	1367	130
6	1988	130
7	2937	130
8	3090	130
9	3337	130
10	3652	130
11	4133	130
12	4812	130
13	5706	130
14	6350	130
15	6861	130
16	7262	130
17	7641	130
18	7859	130

Stop Event

1×	node limit

Counts

35 → 31

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 -1/36 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 -1/36 (pow.f64 x 3)) (+.f64 (.f64 1/2880 (pow.f64 x 5)) (*.f64 2/3 x)))
(+.f64 (.f64 -1/36 (pow.f64 x 3)) (+.f64 (.f64 1/2880 (pow.f64 x 5)) (+.f64 (.f64 2/3 x) (.f64 -1/483840 (pow.f64 x 7)))))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 -1/36 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 -1/36 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 -1/36 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x -1/36) 2/3))
(.f64 x (fma.f64 -1/36 (.f64 x x) 2/3))
(+.f64 (.f64 -1/36 (pow.f64 x 3)) (+.f64 (.f64 1/2880 (pow.f64 x 5)) (*.f64 2/3 x)))
(fma.f64 -1/36 (pow.f64 x 3) (fma.f64 1/2880 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 -1/36 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/2880 (pow.f64 x 5))))
(fma.f64 2/3 x (fma.f64 -1/36 (pow.f64 x 3) (*.f64 1/2880 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x -1/36) 2/3) (.f64 1/2880 (pow.f64 x 5)))
(fma.f64 2/3 x (fma.f64 1/2880 (pow.f64 x 5) (*.f64 -1/36 (pow.f64 x 3))))
(+.f64 (.f64 -1/36 (pow.f64 x 3)) (+.f64 (.f64 1/2880 (pow.f64 x 5)) (+.f64 (.f64 2/3 x) (.f64 -1/483840 (pow.f64 x 7)))))
(fma.f64 -1/36 (pow.f64 x 3) (fma.f64 1/2880 (pow.f64 x 5) (fma.f64 2/3 x (*.f64 -1/483840 (pow.f64 x 7)))))
(fma.f64 -1/36 (pow.f64 x 3) (fma.f64 1/2880 (pow.f64 x 5) (fma.f64 -1/483840 (pow.f64 x 7) (*.f64 2/3 x))))
(fma.f64 2/3 x (fma.f64 1/2880 (pow.f64 x 5) (fma.f64 -1/36 (pow.f64 x 3) (*.f64 -1/483840 (pow.f64 x 7)))))
(fma.f64 1/2880 (pow.f64 x 5) (fma.f64 -1/36 (pow.f64 x 3) (fma.f64 -1/483840 (pow.f64 x 7) (*.f64 2/3 x))))
(fma.f64 2/3 x (fma.f64 -1/36 (pow.f64 x 3) (fma.f64 1/2880 (pow.f64 x 5) (*.f64 -1/483840 (pow.f64 x 7)))))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))
(.f64 4/3 (sin.f64 (.f64 1/2 x)))
(.f64 4/3 (sin.f64 (.f64 x 1/2)))

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 x)
✓	0.1b	(*.f64 (sin.f64 x) -3/4)
✓	0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4))
	1.9b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 35 to 20 computations (42.9% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite91.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
381×	`exp-prod_binary64`
259×	`prod-diff_binary64`
249×	`pow2_binary64`
244×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	192	15
2	2603	15

Stop Event

1×	node limit

Counts

2 → 132

Calls

Call 1

Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4))
(*.f64 (sin.f64 x) -3/4)

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sin.f64 x) -3/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) -3/4)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) -3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) -3/4))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) -3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) -3/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sin.f64 x) -3/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 (sin.f64 x) -3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 9/16 (pow.f64 (sin.f64 x) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sin.f64 x) -3/4) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) -3/4)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) -3/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sin.f64 x) -3/4))) 2)) (cbrt.f64 (log.f64 (*.f64 (sin.f64 x) -3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sin.f64 x) -3/4)))) (sqrt.f64 (log.f64 (*.f64 (sin.f64 x) -3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 9/16 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) -3/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) -3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) -3/4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) -3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) -3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sin.f64 x) -3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) -3/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sin.f64 x) -3/4))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sin.f64 x) -3/4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sin.f64 x) -3/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) -3/4)) 1) 1))))))

simplify130.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-def_binary64`
624×	`unswap-sqr_binary64`
521×	`associate-l_binary64`
495×	`sqr-pow_binary64`
351×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	236
1	98	236
2	232	236
3	598	236
4	1239	236
5	2606	236
6	3764	236
7	5036	236
8	5544	236
9	6063	236
10	6525	236
11	7167	236

Stop Event

1×	node limit

Counts

156 → 150

Calls

Call 1

Inputs
(*.f64 -2/3 x)
(+.f64 (.f64 -2/3 x) (.f64 -1/18 (pow.f64 x 3)))
(+.f64 (.f64 -1/180 (pow.f64 x 5)) (+.f64 (.f64 -2/3 x) (*.f64 -1/18 (pow.f64 x 3))))
(+.f64 (.f64 -17/30240 (pow.f64 x 7)) (+.f64 (.f64 -1/180 (pow.f64 x 5)) (+.f64 (.f64 -2/3 x) (.f64 -1/18 (pow.f64 x 3)))))
(*.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 -3/4 x)
(+.f64 (.f64 -3/4 x) (.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 -3/4 x) (+.f64 (.f64 -1/160 (pow.f64 x 5)) (*.f64 1/8 (pow.f64 x 3))))
(+.f64 (.f64 1/6720 (pow.f64 x 7)) (+.f64 (.f64 -3/4 x) (+.f64 (.f64 -1/160 (pow.f64 x 5)) (.f64 1/8 (pow.f64 x 3)))))
(*.f64 -3/4 (sin.f64 x))
(*.f64 -3/4 (sin.f64 x))
(*.f64 -3/4 (sin.f64 x))
(*.f64 -3/4 (sin.f64 x))
(*.f64 -3/4 (sin.f64 x))
(*.f64 -3/4 (sin.f64 x))
(*.f64 -3/4 (sin.f64 x))
(*.f64 -3/4 (sin.f64 x))

Outputs
(*.f64 -2/3 x)
(+.f64 (.f64 -2/3 x) (.f64 -1/18 (pow.f64 x 3)))
(fma.f64 -2/3 x (*.f64 -1/18 (pow.f64 x 3)))
(fma.f64 -1/18 (pow.f64 x 3) (*.f64 -2/3 x))
(.f64 x (fma.f64 x (.f64 x -1/18) -2/3))
(+.f64 (.f64 -1/180 (pow.f64 x 5)) (+.f64 (.f64 -2/3 x) (*.f64 -1/18 (pow.f64 x 3))))
(fma.f64 -1/180 (pow.f64 x 5) (fma.f64 -2/3 x (*.f64 -1/18 (pow.f64 x 3))))
(fma.f64 -1/18 (pow.f64 x 3) (fma.f64 -1/180 (pow.f64 x 5) (*.f64 -2/3 x)))
(fma.f64 x (fma.f64 x (.f64 x -1/18) -2/3) (.f64 -1/180 (pow.f64 x 5)))
(fma.f64 -1/180 (pow.f64 x 5) (.f64 x (fma.f64 x (.f64 x -1/18) -2/3)))
(+.f64 (.f64 -17/30240 (pow.f64 x 7)) (+.f64 (.f64 -1/180 (pow.f64 x 5)) (+.f64 (.f64 -2/3 x) (.f64 -1/18 (pow.f64 x 3)))))
(fma.f64 -17/30240 (pow.f64 x 7) (fma.f64 -1/180 (pow.f64 x 5) (fma.f64 -2/3 x (*.f64 -1/18 (pow.f64 x 3)))))
(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))))
(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 -17/30240 (pow.f64 x 7) (fma.f64 -1/180 (pow.f64 x 5) (.f64 x (fma.f64 x (.f64 x -1/18) -2/3))))
(fma.f64 -1/180 (pow.f64 x 5) (fma.f64 -2/3 x (fma.f64 -1/18 (pow.f64 x 3) (*.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 -3/4 x)
(*.f64 x -3/4)
(+.f64 (.f64 -3/4 x) (.f64 1/8 (pow.f64 x 3)))
(fma.f64 -3/4 x (*.f64 (pow.f64 x 3) 1/8))
(fma.f64 x -3/4 (*.f64 (pow.f64 x 3) 1/8))
(.f64 x (fma.f64 x (.f64 x 1/8) -3/4))
(+.f64 (.f64 -3/4 x) (+.f64 (.f64 -1/160 (pow.f64 x 5)) (*.f64 1/8 (pow.f64 x 3))))
(fma.f64 -3/4 x (fma.f64 -1/160 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 1/8)))
(fma.f64 x -3/4 (fma.f64 (pow.f64 x 3) 1/8 (*.f64 (pow.f64 x 5) -1/160)))
(fma.f64 (pow.f64 x 3) 1/8 (fma.f64 x -3/4 (*.f64 (pow.f64 x 5) -1/160)))
(fma.f64 x (fma.f64 x (.f64 x 1/8) -3/4) (.f64 (pow.f64 x 5) -1/160))
(fma.f64 x -3/4 (fma.f64 (pow.f64 x 5) -1/160 (*.f64 (pow.f64 x 3) 1/8)))
(+.f64 (.f64 1/6720 (pow.f64 x 7)) (+.f64 (.f64 -3/4 x) (+.f64 (.f64 -1/160 (pow.f64 x 5)) (.f64 1/8 (pow.f64 x 3)))))
(fma.f64 1/6720 (pow.f64 x 7) (fma.f64 -3/4 x (fma.f64 -1/160 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 1/8))))
(fma.f64 (pow.f64 x 7) 1/6720 (fma.f64 x -3/4 (fma.f64 (pow.f64 x 3) 1/8 (*.f64 (pow.f64 x 5) -1/160))))
(fma.f64 x -3/4 (fma.f64 (pow.f64 x 7) 1/6720 (fma.f64 (pow.f64 x 3) 1/8 (*.f64 (pow.f64 x 5) -1/160))))
(fma.f64 (pow.f64 x 3) 1/8 (fma.f64 (pow.f64 x 5) -1/160 (fma.f64 (pow.f64 x 7) 1/6720 (*.f64 x -3/4))))
(fma.f64 x -3/4 (fma.f64 (pow.f64 x 3) 1/8 (fma.f64 (pow.f64 x 5) -1/160 (*.f64 (pow.f64 x 7) 1/6720))))
(fma.f64 x -3/4 (fma.f64 (pow.f64 x 5) -1/160 (fma.f64 (pow.f64 x 3) 1/8 (*.f64 (pow.f64 x 7) 1/6720))))
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)
(*.f64 -3/4 (sin.f64 x))
(*.f64 (sin.f64 x) -3/4)

eval138.0ms (1.7%)

Compiler: Compiled 6470 to 4354 computations (32.7% saved)

prune50.0ms (0.6%)

Pruning

16 alts after pruning (9 fresh and 7 done)

	Pruned	Kept	Total
New	325	4	329
Fresh	1	5	6
Picked	0	1	1
Done	0	6	6
Total	326	16	342

Error

Counts

342 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	0.3b	(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
✓	60.6b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
	20.6b	(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))
✓	29.4b	(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)
✓	0.1b	(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
	29.8b	(neg.f64 (-.f64 (/.f64 -4/3 (sin.f64 x)) (/.f64 (/.f64 (cos.f64 x) -3/4) (sin.f64 x))))
	29.7b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
	0.4b	(+.f64 0 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
	61.0b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
✓	46.2b	(fabs.f64 (*.f64 2/3 x))
✓	29.6b	(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4)))
✓	32.1b	(*.f64 2/3 x)
	0.3b	(neg.f64 (pow.f64 (/.f64 -3/4 (tan.f64 (/.f64 x 2))) -1))
	29.6b	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
✓	61.3b	(-.f64 1 1)
	29.0b	(+.f64 0 (-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1))

Compiler

Compiled 160 to 136 computations (15% saved)

regimes136.0ms (1.6%)

Counts

66 → 1

Calls

Call 1

Inputs
(-.f64 1 1)
(*.f64 2/3 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))
(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
(+.f64 0 (-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1))
(cbrt.f64 (*.f64 (pow.f64 x 3) 8/27))
(pow.f64 (sqrt.f64 (*.f64 2/3 x)) 2)
(pow.f64 (cbrt.f64 (*.f64 2/3 x)) 3)
(expm1.f64 (log1p.f64 (/.f64 8/3 (/.f64 4 x))))
(neg.f64 (pow.f64 (/.f64 -3/4 (tan.f64 (/.f64 x 2))) -1))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4)))
(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(/.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 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
(+.f64 0 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (*.f64 8/3 (/.f64 1 (sin.f64 x))))
(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (-.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 (sin.f64 x)) (.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))
(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (+.f64 (.f64 4/9 x) (.f64 8/3 (/.f64 1 x))))
(expm1.f64 (log1p.f64 (*.f64 4/3 (tan.f64 (/.f64 x 2)))))
(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 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 x 1/2)) 2) (sin.f64 x)))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
(/.f64 1 (*.f64 (/.f64 (sin.f64 x) (fma.f64 (cos.f64 x) -1/2 1/2)) 3/8))
(neg.f64 (-.f64 (/.f64 -4/3 (sin.f64 x)) (/.f64 (/.f64 (cos.f64 x) -3/4) (sin.f64 x))))
(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
(-.f64 (/.f64 1/2 (.f64 (sin.f64 x) 3/8)) (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4)))
(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
(.f64 (.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))) (sin.f64 (.f64 x 1/2)))
(/.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 (.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 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
(/.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 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 6) (/.f64 8/3 (sin.f64 x)))
(pow.f64 (.f64 3/8 (.f64 (sin.f64 x) (pow.f64 (sin.f64 (*.f64 x 1/2)) -2))) -1)
(expm1.f64 (log1p.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))
(.f64 (log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x)))))) (/.f64 8/3 (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
(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 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 3) (/.f64 8/3 (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)))
(pow.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 6) (pow.f64 (sin.f64 x) 3)) 1/3)
(/.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)))
(.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 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))

Calls

3 calls:

43.0ms	x
35.0ms	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
33.0ms	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))`
0.1b	1	`(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))`

Compiler

Compiled 832 to 605 computations (27.3% saved)

regimes9.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
0.3b	1	`x`

Compiler

Compiled 53 to 44 computations (17% saved)

regimes8.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

Inputs
(-.f64 1 1)
(*.f64 2/3 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))
(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)

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

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
29.4b	1	`x`

Compiler

Compiled 47 to 39 computations (17% saved)

regimes10.0ms (0.1%)

Accuracy

Total -30.1b remaining (-93.8%)

Threshold costs -30.1b (-93.8%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(*.f64 2/3 x)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
32.1b	1	`x`

Compiler

Compiled 41 to 34 computations (17.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`+-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	32
1	24	32

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)
(*.f64 2/3 x)
(-.f64 1 1)

Outputs
(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
(/.f64 (tan.f64 (/.f64 x 2)) 3/4)
(*.f64 (tan.f64 (/.f64 x 2)) 4/3)
(/.f64 (sin.f64 (*.f64 x 1/2)) 3/4)
(*.f64 2/3 x)
(*.f64 x 2/3)
(-.f64 1 1)
0

Compiler

Compiled 27 to 23 computations (14.8% saved)

soundness12.0ms (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

Compiler

Compiled 83 to 68 computations (18.1% saved)

end36.0ms (0.4%)

Compiler: Compiled 23 to 19 computations (17.4% saved)