Details

analyze409.0ms (4.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.7s (39%)

Results

1.5s	5198×	body	256	valid
1.4s	2027×	body	1024	valid
720.0ms	1019×	body	512	valid
16.0ms	12×	body	2048	valid

Bogosity

preprocess36.0ms (0.4%)

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)

simplify16.0ms (0.2%)

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

17.4b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.6b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))
▶	17.6b	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize28.0ms (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)))
✓	0.4b	(/.f64 8/3 (sin.f64 x))
✓	17.4b	(.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)

series8.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

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

rewrite80.0ms (0.9%)

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))))))
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Outputs

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#<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 (0.7%)

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)

localize29.0ms (0.3%)

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)))
✓	17.4b	(/.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)))

✓

17.4b

(/.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)

series5.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite102.0ms (1.1%)

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))))))) 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Outputs

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

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

((#(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))))))

simplify73.0ms (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))

eval102.0ms (1.1%)

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

prune85.0ms (0.9%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	228	37	265
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	230	37	267

Error

0.0b

Counts

267 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	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))))
	24.7b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (cbrt.f64 (pow.f64 (/.f64 8/3 (sin.f64 x)) 3)))
	44.8b	(/.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/18) 2/3))) (sin.f64 x))
	34.1b	(/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 8/3 (-.f64 1/2 (.f64 1/2 (cos.f64 x)))))) 1) (sin.f64 x))
	24.8b	(.f64 (sqrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 4)) (/.f64 8/3 (sin.f64 x)))
	33.9b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
	0.6b	(.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)))
	44.5b	(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
	32.9b	(pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)
	34.0b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
	27.5b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
	32.9b	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
	41.9b	(.f64 (pow.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 4) (/.f64 8/3 (sin.f64 x)))
	27.5b	(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
	34.2b	(pow.f64 (cbrt.f64 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) 3)
▶	0.5b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) 1) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
	17.6b	(/.f64 (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
	17.6b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
	44.6b	(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
	27.5b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
	35.2b	(log1p.f64 (expm1.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)))
	34.0b	(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
▶	33.9b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
▶	27.3b	(*.f64 2/3 x)
▶	27.7b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
	34.0b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
	34.0b	(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))
	34.0b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
	44.1b	(.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))))
	17.6b	(/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 2) (sin.f64 x))
	44.4b	(/.f64 (.f64 (.f64 x 4/3) (sin.f64 (*.f64 x 1/2))) (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))))
	17.6b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
	34.0b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	34.0b	(+.f64 0 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))
▶	17.6b	(/.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)

localize27.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 51 to 38 computations (25.5% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite86.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

549×	`log-prod_binary64`
414×	`exp-prod_binary64`
314×	`pow-prod-down_binary64`
283×	`pow2_binary64`
199×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	254	37
2	2890	37

Stop Event

1×	node limit

Counts

3 → 149

Calls

Call 1

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

Outputs

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

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

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

730×	`distribute-lft-out_binary64`
730×	`fma-def_binary64`
518×	`unswap-sqr_binary64`
503×	`associate-l_binary64`
395×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	464
1	148	462
2	356	458
3	1036	458
4	3335	458
5	5254	458
6	7745	458

Stop Event

1×	node limit

Counts

185 → 177

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)))
1/2
(+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (.f64 5/768 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 2))))
(+.f64 1/2 (+.f64 (.f64 61/92160 (pow.f64 x 6)) (+.f64 (.f64 5/768 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 2)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.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 (.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 -1/18 (.f64 x x) 4/3) (.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 -1/18 (pow.f64 x 3) (fma.f64 1/1440 (pow.f64 x 5) (*.f64 -1/241920 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 -1/18 (.f64 x x) 4/3) (fma.f64 1/1440 (pow.f64 x 5) (.f64 -1/241920 (pow.f64 x 7))))
(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))))
(.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 (.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 (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 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 3) 1/18 (fma.f64 x 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 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)))
(.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)))
1/2
(+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))
(+.f64 1/2 (.f64 1/16 (.f64 x x)))
(fma.f64 1/16 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 x 1/16) 1/2)
(+.f64 1/2 (+.f64 (.f64 5/768 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 2))))
(+.f64 1/2 (fma.f64 5/768 (pow.f64 x 4) (.f64 1/16 (.f64 x x))))
(+.f64 1/2 (fma.f64 5/768 (pow.f64 x 4) (.f64 x (.f64 x 1/16))))
(fma.f64 x (*.f64 x 1/16) (fma.f64 5/768 (pow.f64 x 4) 1/2))
(+.f64 1/2 (+.f64 (.f64 61/92160 (pow.f64 x 6)) (+.f64 (.f64 5/768 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 2)))))
(+.f64 1/2 (fma.f64 61/92160 (pow.f64 x 6) (fma.f64 5/768 (pow.f64 x 4) (.f64 1/16 (.f64 x x)))))
(+.f64 1/2 (fma.f64 61/92160 (pow.f64 x 6) (fma.f64 5/768 (pow.f64 x 4) (.f64 x (.f64 x 1/16)))))
(fma.f64 61/92160 (pow.f64 x 6) (fma.f64 x (*.f64 x 1/16) (fma.f64 5/768 (pow.f64 x 4) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 5/768) 1/16) (fma.f64 61/92160 (pow.f64 x 6) 1/2))
(fma.f64 x (*.f64 x 1/16) (fma.f64 61/92160 (pow.f64 x 6) (fma.f64 5/768 (pow.f64 x 4) 1/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series3.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite44.0ms (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))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

Calls

Call 1

Inputs

Outputs

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 x) 3/8)
✓	0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
✓	3.0b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 34 to 21 computations (38.2% saved)

series5.0ms (0.1%)

Counts

3 → 28

Calls

9 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))
1.0ms	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)

rewrite107.0ms (1.1%)

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	26
1	236	26
2	3117	21

Stop Event

1×	node limit

Counts

3 → 180

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)

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) 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((#(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))))))

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
758×	`distribute-lft-out_binary64`
714×	`distribute-rgt-out_binary64`
705×	`associate-l_binary64`
543×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	306
1	159	306
2	378	306
3	1157	306
4	4422	306
5	6888	306
6	7683	306

Stop Event

1×	node limit

Counts

208 → 208

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))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/24 (pow.f64 x 4))))
(+.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 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 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) (*.f64 x 2/3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 x 2/3 (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 x 2/3))))
(fma.f64 x 2/3 (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 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 x 3/8 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 (pow.f64 x 5) 1/320)))
(fma.f64 x 3/8 (fma.f64 1/320 (pow.f64 x 5) (*.f64 (pow.f64 x 3) -1/16)))
(+.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 1/320 (pow.f64 x 5) (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)

localize25.0ms (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))
✓	17.4b	(/.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)

rewrite92.0ms (1%)

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))))))

simplify103.0ms (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)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 8/3 (sin.f64 x))
✓	0.5b	(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
✓	10.1b	(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) 1/3)
✓	17.4b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 46 to 35 computations (23.9% saved)

series13.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
2.0ms	x	@	-inf	(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) 1/3)
2.0ms	x	@	inf	(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) 1/3)
2.0ms	x	@	0	(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) 1/3)
1.0ms	x	@	-inf	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))

rewrite85.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`log-prod_binary64`
318×	`pow2_binary64`
292×	`pow-prod-down_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	284	35
2	3152	35

Stop Event

1×	node limit

Counts

3 → 91

Calls

Call 1

Inputs
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) 1/3)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)

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 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 (-.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 (/.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 (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 (-.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 +.f64 0 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (*.f64 1/2 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 4) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (pow.f64 (sin.f64 (*.f64 x 1/2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3/2) (sqrt.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 5) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (cos.f64 (-.f64 (*.f64 x 1/2) (*.f64 x 1/2))) (cos.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (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 (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 12 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1/6))))) (#(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 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)) 1/6) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (pow.f64 (sin.f64 (*.f64 x 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) (pow.f64 (sin.f64 (*.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 4) 1) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) 4) 2) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 5) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 12))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 18))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (sin.f64 (*.f64 x 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 18)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 1) 6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)) 1/6) 6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 6)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 3) 2))))))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

834×	`associate-/l*_binary64`
567×	`associate-/r*_binary64`
375×	`*-commutative_binary64`
251×	`fma-def_binary64`
248×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	548
1	197	534
2	505	534
3	1917	534
4	6155	534
5	7358	534

Stop Event

1×	node limit

Counts

127 → 119

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (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 (cbrt.f64 1/64) (pow.f64 x 2))
(+.f64 (.f64 (cbrt.f64 1/64) (pow.f64 x 2)) (.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2))))
(+.f64 (.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2))) (+.f64 (.f64 (cbrt.f64 1/64) (pow.f64 x 2)) (*.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)))))
(+.f64 (.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2))) (+.f64 (.f64 (cbrt.f64 1/64) (pow.f64 x 2)) (+.f64 (.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2))) (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 1/452984832 (/.f64 1 (pow.f64 (cbrt.f64 1/64) 6))) 11/967680) (pow.f64 x 8)) (pow.f64 (cbrt.f64 1/64) 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)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(*.f64 1/64 (pow.f64 x 6))
(+.f64 (.f64 -1/256 (pow.f64 x 8)) (.f64 1/64 (pow.f64 x 6)))
(+.f64 (.f64 7/15360 (pow.f64 x 10)) (+.f64 (.f64 -1/256 (pow.f64 x 8)) (*.f64 1/64 (pow.f64 x 6))))
(+.f64 (.f64 7/15360 (pow.f64 x 10)) (+.f64 (.f64 -1/256 (pow.f64 x 8)) (+.f64 (.f64 -1/30240 (pow.f64 x 12)) (.f64 1/64 (pow.f64 x 6)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)

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 (.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 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(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))))
(.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 (cbrt.f64 1/64) (pow.f64 x 2))
(.f64 (cbrt.f64 1/64) (.f64 x x))
(.f64 x (.f64 x (cbrt.f64 1/64)))
(+.f64 (.f64 (cbrt.f64 1/64) (pow.f64 x 2)) (.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2))))
(fma.f64 (cbrt.f64 1/64) (.f64 x x) (.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2))))
(fma.f64 (cbrt.f64 1/64) (*.f64 x x) (/.f64 -1/768 (/.f64 (pow.f64 (cbrt.f64 1/64) 2) (pow.f64 x 4))))
(fma.f64 x (*.f64 x (cbrt.f64 1/64)) (/.f64 -1/768 (/.f64 (pow.f64 (cbrt.f64 1/64) 2) (pow.f64 x 4))))
(fma.f64 x (.f64 x (cbrt.f64 1/64)) (/.f64 (.f64 -1/768 (pow.f64 x 4)) (pow.f64 (cbrt.f64 1/64) 2)))
(+.f64 (.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2))) (+.f64 (.f64 (cbrt.f64 1/64) (pow.f64 x 2)) (*.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)))))
(fma.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2)) (fma.f64 (cbrt.f64 1/64) (.f64 x x) (.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)))))
(fma.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2)) (fma.f64 (cbrt.f64 1/64) (*.f64 x x) (/.f64 -1/768 (/.f64 (pow.f64 (cbrt.f64 1/64) 2) (pow.f64 x 4)))))
(fma.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)) (fma.f64 x (.f64 x (cbrt.f64 1/64)) (/.f64 (.f64 1/23040 (pow.f64 x 6)) (pow.f64 (cbrt.f64 1/64) 2))))
(fma.f64 x (*.f64 x (cbrt.f64 1/64)) (fma.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)) (/.f64 (pow.f64 x 6) (/.f64 (pow.f64 (cbrt.f64 1/64) 2) 1/23040))))
(+.f64 (.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2))) (+.f64 (.f64 (cbrt.f64 1/64) (pow.f64 x 2)) (+.f64 (.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2))) (.f64 1/3 (/.f64 (.f64 (-.f64 (.f64 1/452984832 (/.f64 1 (pow.f64 (cbrt.f64 1/64) 6))) 11/967680) (pow.f64 x 8)) (pow.f64 (cbrt.f64 1/64) 2))))))
(fma.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2)) (fma.f64 (cbrt.f64 1/64) (.f64 x x) (fma.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)) (.f64 1/3 (/.f64 (*.f64 (+.f64 (/.f64 1/452984832 (pow.f64 (cbrt.f64 1/64) 6)) -11/967680) (pow.f64 x 8)) (pow.f64 (cbrt.f64 1/64) 2))))))
(fma.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2)) (fma.f64 (cbrt.f64 1/64) (.f64 x x) (fma.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)) (/.f64 (.f64 -1/1290240 (pow.f64 x 8)) (pow.f64 (cbrt.f64 1/64) 2)))))
(fma.f64 x (.f64 x (cbrt.f64 1/64)) (fma.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2)) (fma.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)) (.f64 (/.f64 -1/1290240 (pow.f64 (cbrt.f64 1/64) 2)) (pow.f64 x 8)))))
(fma.f64 x (.f64 x (cbrt.f64 1/64)) (fma.f64 1/23040 (/.f64 (pow.f64 x 6) (pow.f64 (cbrt.f64 1/64) 2)) (fma.f64 -1/768 (/.f64 (pow.f64 x 4) (pow.f64 (cbrt.f64 1/64) 2)) (.f64 (pow.f64 x 8) (/.f64 -1/1290240 (pow.f64 (cbrt.f64 1/64) 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)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(*.f64 1/64 (pow.f64 x 6))
(+.f64 (.f64 -1/256 (pow.f64 x 8)) (.f64 1/64 (pow.f64 x 6)))
(fma.f64 -1/256 (pow.f64 x 8) (*.f64 1/64 (pow.f64 x 6)))
(fma.f64 1/64 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1/256))
(+.f64 (.f64 7/15360 (pow.f64 x 10)) (+.f64 (.f64 -1/256 (pow.f64 x 8)) (*.f64 1/64 (pow.f64 x 6))))
(fma.f64 7/15360 (pow.f64 x 10) (fma.f64 -1/256 (pow.f64 x 8) (*.f64 1/64 (pow.f64 x 6))))
(fma.f64 7/15360 (pow.f64 x 10) (fma.f64 1/64 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1/256)))
(fma.f64 1/64 (pow.f64 x 6) (fma.f64 (pow.f64 x 8) -1/256 (*.f64 7/15360 (pow.f64 x 10))))
(fma.f64 1/64 (pow.f64 x 6) (fma.f64 7/15360 (pow.f64 x 10) (*.f64 (pow.f64 x 8) -1/256)))
(+.f64 (.f64 7/15360 (pow.f64 x 10)) (+.f64 (.f64 -1/256 (pow.f64 x 8)) (+.f64 (.f64 -1/30240 (pow.f64 x 12)) (.f64 1/64 (pow.f64 x 6)))))
(fma.f64 7/15360 (pow.f64 x 10) (fma.f64 -1/256 (pow.f64 x 8) (fma.f64 -1/30240 (pow.f64 x 12) (*.f64 1/64 (pow.f64 x 6)))))
(fma.f64 7/15360 (pow.f64 x 10) (fma.f64 (pow.f64 x 8) -1/256 (fma.f64 1/64 (pow.f64 x 6) (*.f64 -1/30240 (pow.f64 x 12)))))
(fma.f64 (pow.f64 x 8) -1/256 (fma.f64 7/15360 (pow.f64 x 10) (fma.f64 1/64 (pow.f64 x 6) (*.f64 -1/30240 (pow.f64 x 12)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 6)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 6)

eval508.0ms (5.4%)

Compiler: Compiled 14031 to 10016 computations (28.6% saved)

prune171.0ms (1.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	692	14	706
Fresh	32	0	32
Picked	1	0	1
Done	2	2	4
Total	727	16	743

Error

Counts

743 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	23.0b	(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))
▶	0.1b	(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
	59.5b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
▶	32.5b	(log.f64 (exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
▶	59.2b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
	33.9b	(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4)))
	27.7b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (*.f64 (/.f64 1 (sin.f64 x)) 8/3))
	41.9b	(pow.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3) 1/3)
	27.5b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
✓	27.3b	(*.f64 2/3 x)
▶	0.2b	(pow.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) -1)
	45.5b	(fabs.f64 (*.f64 2/3 x))
	33.9b	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
✓	17.6b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
▶	0.4b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
	34.0b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))

Compiler

Compiled 330 to 283 computations (14.2% saved)

localize16.0ms (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)

series8.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	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)

rewrite63.0ms (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)))))))

simplify160.0ms (1.7%)

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))))

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(*.f64 2/3 x)
✓	3.6b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite59.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

55 → 43

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite53.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify162.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

25 → 22

Calls

Call 1

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

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

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (tan.f64 (/.f64 x 2)) 3/4)
✓	0.2b	(pow.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) -1)
✓	0.3b	(/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))

Compiler

Compiled 37 to 31 computations (16.2% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(pow.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) -1)
1.0ms	x	@	-inf	(pow.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) -1)
1.0ms	x	@	inf	(/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
1.0ms	x	@	-inf	(/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
1.0ms	x	@	0	(/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

949×	`pow1_binary64`
891×	`add-log-exp_binary64`
890×	`log1p-expm1-u_binary64`
890×	`expm1-log1p-u_binary64`
113×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	240	18
2	2754	18

Stop Event

1×	node limit

Counts

2 → 64

Calls

Call 1

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

Outputs

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

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

simplify154.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-def_binary64`
675×	`sqr-pow_binary64`
624×	`unswap-sqr_binary64`
528×	`cube-prod_binary64`
442×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	381
1	112	379
2	243	379
3	615	379
4	1052	379
5	2140	379
6	2907	379
7	3856	379
8	4009	379
9	4255	379
10	4570	379
11	5051	379
12	5730	379
13	6624	379
14	7268	379
15	7775	379

Stop Event

1×	node limit

Counts

88 → 83

Calls

Call 1

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

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (tan.f64 (/.f64 x 2)) 3/4)
✓	0.3b	(exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
✓	3.7b	(log.f64 (exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))

Compiler

Compiled 32 to 26 computations (18.8% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(log.f64 (exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
0.0ms	x	@	0	(exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
0.0ms	x	@	-inf	(exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
0.0ms	x	@	inf	(exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
0.0ms	x	@	inf	(log.f64 (exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`pow1_binary64`
752×	`add-log-exp_binary64`
752×	`log1p-expm1-u_binary64`
752×	`expm1-log1p-u_binary64`
740×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	182	20
2	2054	20

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

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

Outputs

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

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

simplify108.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1049×	`fma-def_binary64`
451×	`unswap-sqr_binary64`
410×	`sqr-pow_binary64`
369×	`associate-/l*_binary64`
276×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	387
1	98	383
2	229	383
3	651	377
4	1532	376
5	2561	374
6	3709	374
7	4498	374
8	6235	374
9	6766	374
10	7712	374

Stop Event

1×	node limit

Counts

79 → 73

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))))
1
(+.f64 (*.f64 2/3 x) 1)
(+.f64 (.f64 2/3 x) (+.f64 1 (.f64 2/9 (pow.f64 x 2))))
(+.f64 (.f64 17/162 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (+.f64 1 (*.f64 2/9 (pow.f64 x 2)))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(exp.f64 (.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 1/18 (.f64 x x) 2/3))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 3))))
(fma.f64 x (fma.f64 1/18 (.f64 x x) 2/3) (.f64 1/180 (pow.f64 x 5)))
(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 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.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 (fma.f64 1/18 (.f64 x x) 2/3))))
(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)))))
(.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))))
1
(+.f64 (*.f64 2/3 x) 1)
(fma.f64 2/3 x 1)
(+.f64 (.f64 2/3 x) (+.f64 1 (.f64 2/9 (pow.f64 x 2))))
(+.f64 (fma.f64 2/3 x 1) (.f64 2/9 (.f64 x x)))
(fma.f64 2/3 x (fma.f64 2/9 (*.f64 x x) 1))
(fma.f64 x (fma.f64 x 2/9 2/3) 1)
(+.f64 (.f64 17/162 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (+.f64 1 (*.f64 2/9 (pow.f64 x 2)))))
(fma.f64 17/162 (pow.f64 x 3) (+.f64 (fma.f64 2/3 x 1) (.f64 2/9 (.f64 x x))))
(fma.f64 (pow.f64 x 3) 17/162 (fma.f64 2/3 x (fma.f64 2/9 (*.f64 x x) 1)))
(fma.f64 2/3 x (fma.f64 (pow.f64 x 3) 17/162 (fma.f64 2/9 (*.f64 x x) 1)))
(fma.f64 x (fma.f64 x 2/9 2/3) (fma.f64 (pow.f64 x 3) 17/162 1))
(fma.f64 x (+.f64 2/3 (*.f64 x (fma.f64 x 17/162 2/9))) 1)
(fma.f64 x (fma.f64 x (fma.f64 x 17/162 2/9) 2/3) 1)
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))
(exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (exp.f64 4/3) (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2))))

eval124.0ms (1.3%)

Compiler: Compiled 4029 to 3465 computations (14% saved)

prune60.0ms (0.6%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	334	8	342
Fresh	5	4	9
Picked	1	0	1
Done	3	3	6
Total	343	15	358

Error

Counts

358 → 15

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)
	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/4 (cos.f64 (*.f64 x 1/2))))
▶	45.5b	(fabs.f64 (*.f64 2/3 x))
	61.1b	(log.f64 1)
	27.7b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (*.f64 (/.f64 1 (sin.f64 x)) 8/3))
	0.4b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))
▶	0.3b	(pow.f64 (.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 3/4) -1)
▶	0.3b	(/.f64 1 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))
▶	59.5b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
	0.4b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
✓	59.2b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
	27.2b	(pow.f64 (/.f64 3/2 x) -1)
✓	27.3b	(*.f64 2/3 x)
✓	0.4b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
	34.0b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))

Compiler

Compiled 269 to 230 computations (14.5% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite55.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`pow1_binary64`
639×	`add-log-exp_binary64`
639×	`log1p-expm1-u_binary64`
639×	`expm1-log1p-u_binary64`
629×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	151	9
2	1723	9

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(/.f64 (tan.f64 (*.f64 x 1/2)) 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)))))))

simplify165.0ms (1.7%)

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))))

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (*.f64 2/3 x)))
	0.3b	(*.f64 2/3 x)
✓	3.5b	(-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (*.f64 2/3 x))) 1)
✓	12.2b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))

Compiler

Compiled 64 to 53 computations (17.2% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite101.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

792×	`fma-def_binary64`
501×	`log-prod_binary64`
318×	`fma-neg_binary64`
261×	`pow2_binary64`
180×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	237	23
2	3633	23

Stop Event

1×	node limit

Counts

3 → 284

Calls

Call 1

Inputs

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

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

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

simplify172.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
609×	`associate-l_binary64`
513×	`fma-def_binary64`
490×	`cube-prod_binary64`
479×	`fabs-mul_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	293
1	29	291
2	48	268
3	100	228
4	224	228
5	607	228
6	2006	228
7	3349	228
8	3555	228
9	3768	228
10	3988	228
11	4305	228
12	4707	228
13	5218	228
14	5787	228
15	6475	228
16	7308	228
17	7700	228
18	7990	228

Stop Event

1×	node limit

Counts

320 → 295

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)
(*.f64 4/3 x)
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(*.f64 4/9 (pow.f64 x 2))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(*.f64 4/9 (pow.f64 x 2))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
1
(+.f64 1 (*.f64 4/3 x))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(*.f64 4/9 (pow.f64 x 2))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(*.f64 4/9 (pow.f64 x 2))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 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)
(*.f64 4/3 x)
(*.f64 x 4/3)
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(*.f64 4/9 (pow.f64 x 2))
(.f64 4/9 (.f64 x x))
(.f64 x (.f64 x 4/9))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(*.f64 4/9 (pow.f64 x 2))
(.f64 4/9 (.f64 x x))
(.f64 x (.f64 x 4/9))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
1
(+.f64 1 (*.f64 4/3 x))
(+.f64 (*.f64 x 4/3) 1)
(fma.f64 x 4/3 1)
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 (fma.f64 4/9 (.f64 x x) (.f64 x 4/3)) 1)
(+.f64 (.f64 x (.f64 x 4/9)) (fma.f64 x 4/3 1))
(fma.f64 x (*.f64 x 4/9) (fma.f64 x 4/3 1))
(fma.f64 x (fma.f64 x 4/9 4/3) 1)
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 (fma.f64 4/9 (.f64 x x) (.f64 x 4/3)) 1)
(+.f64 (.f64 x (.f64 x 4/9)) (fma.f64 x 4/3 1))
(fma.f64 x (*.f64 x 4/9) (fma.f64 x 4/3 1))
(fma.f64 x (fma.f64 x 4/9 4/3) 1)
(*.f64 4/9 (pow.f64 x 2))
(.f64 4/9 (.f64 x x))
(.f64 x (.f64 x 4/9))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 (fma.f64 4/9 (.f64 x x) (.f64 x 4/3)) 1)
(+.f64 (.f64 x (.f64 x 4/9)) (fma.f64 x 4/3 1))
(fma.f64 x (*.f64 x 4/9) (fma.f64 x 4/3 1))
(fma.f64 x (fma.f64 x 4/9 4/3) 1)
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 (fma.f64 4/9 (.f64 x x) (.f64 x 4/3)) 1)
(+.f64 (.f64 x (.f64 x 4/9)) (fma.f64 x 4/3 1))
(fma.f64 x (*.f64 x 4/9) (fma.f64 x 4/3 1))
(fma.f64 x (fma.f64 x 4/9 4/3) 1)
(*.f64 4/9 (pow.f64 x 2))
(.f64 4/9 (.f64 x x))
(.f64 x (.f64 x 4/9))
(+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x))
(fma.f64 4/9 (.f64 x x) (.f64 x 4/3))
(.f64 x (+.f64 4/3 (.f64 x 4/9)))
(*.f64 x (fma.f64 x 4/9 4/3))
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 (fma.f64 4/9 (.f64 x x) (.f64 x 4/3)) 1)
(+.f64 (.f64 x (.f64 x 4/9)) (fma.f64 x 4/3 1))
(fma.f64 x (*.f64 x 4/9) (fma.f64 x 4/3 1))
(fma.f64 x (fma.f64 x 4/9 4/3) 1)
(+.f64 1 (+.f64 (.f64 4/9 (pow.f64 x 2)) (.f64 4/3 x)))
(+.f64 (fma.f64 4/9 (.f64 x x) (.f64 x 4/3)) 1)
(+.f64 (.f64 x (.f64 x 4/9)) (fma.f64 x 4/3 1))
(fma.f64 x (*.f64 x 4/9) (fma.f64 x 4/3 1))
(fma.f64 x (fma.f64 x 4/9 4/3) 1)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 10 to 7 computations (30% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 3/4 (tan.f64 (*.f64 x 1/2)))
✓	0.2b	(/.f64 1 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))

Compiler

Compiled 26 to 21 computations (19.2% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite73.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

838×	`pow1_binary64`
783×	`add-log-exp_binary64`
783×	`log1p-expm1-u_binary64`
783×	`expm1-log1p-u_binary64`
769×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	192	18
2	2203	18

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

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

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

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

simplify159.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-def_binary64`
675×	`sqr-pow_binary64`
624×	`unswap-sqr_binary64`
528×	`cube-prod_binary64`
439×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	381
1	112	379
2	243	379
3	621	379
4	1060	379
5	2140	379
6	2912	379
7	3861	379
8	4014	379
9	4261	379
10	4576	379
11	5057	379
12	5736	379
13	6630	379
14	7274	379
15	7783	379

Stop Event

1×	node limit

Counts

71 → 65

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))))
(/.f64 3/2 x)
(+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (*.f64 3/2 (/.f64 1 x))))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 -1/20160 (pow.f64 x 5)))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.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 1/18 (.f64 x x) 2/3))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (*.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 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 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 1/18 (.f64 x x) 2/3))))
(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 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))))
(.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))))
(/.f64 3/2 x)
(+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))
(fma.f64 -1/8 x (/.f64 3/2 x))
(fma.f64 x -1/8 (/.f64 3/2 x))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (*.f64 3/2 (/.f64 1 x))))
(fma.f64 -1/8 x (fma.f64 -1/480 (pow.f64 x 3) (/.f64 3/2 x)))
(fma.f64 x -1/8 (fma.f64 (pow.f64 x 3) -1/480 (/.f64 3/2 x)))
(fma.f64 (pow.f64 x 3) -1/480 (fma.f64 x -1/8 (/.f64 3/2 x)))
(fma.f64 x (fma.f64 -1/480 (*.f64 x x) -1/8) (/.f64 3/2 x))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 -1/20160 (pow.f64 x 5)))))
(fma.f64 -1/8 x (fma.f64 -1/480 (pow.f64 x 3) (+.f64 (/.f64 3/2 x) (*.f64 (pow.f64 x 5) -1/20160))))
(fma.f64 x -1/8 (fma.f64 (pow.f64 x 3) -1/480 (fma.f64 (pow.f64 x 5) -1/20160 (/.f64 3/2 x))))
(fma.f64 x (fma.f64 -1/480 (*.f64 x x) -1/8) (fma.f64 (pow.f64 x 5) -1/20160 (/.f64 3/2 x)))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (cos.f64 (.f64 x 1/2)) (/.f64 (sin.f64 (.f64 x 1/2)) 3/4))
(.f64 (cos.f64 (.f64 x 1/2)) (/.f64 3/4 (sin.f64 (*.f64 x 1/2))))

localize23.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (tan.f64 (*.f64 x 1/2)))
✓	0.2b	(pow.f64 (.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 3/4) -1)
✓	0.3b	(.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 3/4)

Compiler

Compiled 37 to 31 computations (16.2% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite73.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`pow1_binary64`
882×	`add-log-exp_binary64`
880×	`log1p-expm1-u_binary64`
880×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	228	27
2	2496	27

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

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

Outputs

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

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

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

simplify150.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1089×	`fma-def_binary64`
672×	`sqr-pow_binary64`
624×	`unswap-sqr_binary64`
577×	`associate-l_binary64`
388×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	544
1	144	540
2	327	540
3	849	540
4	1456	540
5	2869	540
6	3344	540
7	4293	540
8	4458	540
9	4706	540
10	5021	540
11	5894	540
12	6564	540
13	7437	540

Stop Event

1×	node limit

Counts

99 → 91

Calls

Call 1

Inputs
(/.f64 3/2 x)
(+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (*.f64 3/2 (/.f64 1 x))))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 -1/20160 (pow.f64 x 5)))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 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 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))))
(/.f64 2 x)
(+.f64 (.f64 -1/6 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/15120 (pow.f64 x 5)))))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))

Outputs
(/.f64 3/2 x)
(+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))
(fma.f64 -1/8 x (/.f64 3/2 x))
(fma.f64 x -1/8 (/.f64 3/2 x))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (*.f64 3/2 (/.f64 1 x))))
(fma.f64 -1/8 x (fma.f64 -1/480 (pow.f64 x 3) (/.f64 3/2 x)))
(fma.f64 x -1/8 (fma.f64 -1/480 (pow.f64 x 3) (/.f64 3/2 x)))
(fma.f64 x (fma.f64 x (*.f64 x -1/480) -1/8) (/.f64 3/2 x))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -1/480 (pow.f64 x 3)) (+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 -1/20160 (pow.f64 x 5)))))
(fma.f64 -1/8 x (+.f64 (fma.f64 -1/480 (pow.f64 x 3) (/.f64 3/2 x)) (*.f64 -1/20160 (pow.f64 x 5))))
(fma.f64 x -1/8 (fma.f64 -1/480 (pow.f64 x 3) (fma.f64 -1/20160 (pow.f64 x 5) (/.f64 3/2 x))))
(fma.f64 x (fma.f64 x (*.f64 x -1/480) -1/8) (fma.f64 -1/20160 (pow.f64 x 5) (/.f64 3/2 x)))
(fma.f64 -1/20160 (pow.f64 x 5) (fma.f64 x (fma.f64 x (*.f64 x -1/480) -1/8) (/.f64 3/2 x)))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(.f64 3/4 (/.f64 (cos.f64 (.f64 x 1/2)) (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 1/18 (.f64 x x) 2/3))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 (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)))
(fma.f64 x (fma.f64 1/18 (.f64 x 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 17/30240 (pow.f64 x 7) (fma.f64 (pow.f64 x 5) 1/180 (*.f64 x 2/3))))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 5) 1/180 (fma.f64 x 2/3 (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 5) 1/180 (fma.f64 (pow.f64 x 3) 1/18 (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 (pow.f64 x 5) 1/180 (fma.f64 17/30240 (pow.f64 x 7) (.f64 x (fma.f64 x (.f64 x 1/18) 2/3))))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(.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 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (cos.f64 (.f64 x 1/2)) 4/3))
(/.f64 2 x)
(+.f64 (.f64 -1/6 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/6 x (/.f64 2 x))
(fma.f64 x -1/6 (/.f64 2 x))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/360 (pow.f64 x 3) (fma.f64 -1/6 x (/.f64 2 x)))
(fma.f64 (pow.f64 x 3) -1/360 (fma.f64 x -1/6 (/.f64 2 x)))
(fma.f64 x -1/6 (fma.f64 (pow.f64 x 3) -1/360 (/.f64 2 x)))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/15120 (pow.f64 x 5)))))
(fma.f64 -1/360 (pow.f64 x 3) (+.f64 (fma.f64 -1/6 x (/.f64 2 x)) (*.f64 (pow.f64 x 5) -1/15120)))
(fma.f64 (pow.f64 x 3) -1/360 (fma.f64 x -1/6 (fma.f64 (pow.f64 x 5) -1/15120 (/.f64 2 x))))
(fma.f64 x -1/6 (fma.f64 (pow.f64 x 3) -1/360 (fma.f64 (pow.f64 x 5) -1/15120 (/.f64 2 x))))
(fma.f64 (pow.f64 x 3) -1/360 (fma.f64 (pow.f64 x 5) -1/15120 (fma.f64 x -1/6 (/.f64 2 x))))
(fma.f64 x (fma.f64 x (*.f64 x -1/360) -1/6) (fma.f64 (pow.f64 x 5) -1/15120 (/.f64 2 x)))
(fma.f64 x (fma.f64 -1/360 (*.f64 x x) -1/6) (fma.f64 (pow.f64 x 5) -1/15120 (/.f64 2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))

eval387.0ms (4.1%)

Compiler: Compiled 11160 to 9504 computations (14.8% saved)

prune86.0ms (0.9%)

Pruning

17 alts after pruning (11 fresh and 6 done)

	Pruned	Kept	Total
New	577	6	583
Fresh	2	5	7
Picked	1	0	1
Done	1	6	7
Total	581	17	598

Error

Counts

598 → 17

Alt Table

Click to see full alt table

Status	Error	Program
	0.3b	(/.f64 1 (.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 3/4))
✓	0.1b	(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)
	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/4 (cos.f64 (*.f64 x 1/2))))
	27.7b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (*.f64 (/.f64 1 (sin.f64 x)) 8/3))
	0.4b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))
	61.1b	(/.f64 (.f64 x (.f64 x 4/9)) (+.f64 (+.f64 1 (*.f64 2/3 x)) 1))
✓	0.4b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
	26.3b	(/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
✓	0.3b	(/.f64 1 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))
✓	59.5b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
	0.4b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 4/3 (cos.f64 (*.f64 x 1/2))))
✓	59.2b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
✓	27.3b	(*.f64 2/3 x)
	0.4b	(/.f64 4/3 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
	26.7b	(/.f64 1 (+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x))))
	27.2b	(/.f64 1 (/.f64 3/2 x))
	34.0b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))

Compiler

Compiled 183 to 155 computations (15.3% saved)

regimes109.0ms (1.2%)

Counts

67 → 1

Calls

Call 1

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

Calls

3 calls:

32.0ms	x
27.0ms	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
24.0ms	(/.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 818 to 613 computations (25.1% saved)

regimes23.0ms (0.2%)

Counts

10 → 3

Calls

Call 1

Inputs
(*.f64 2/3 x)
(/.f64 1 (/.f64 3/2 x))
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
(/.f64 1 (+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x))))
(/.f64 (.f64 x (.f64 x 4/9)) (+.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))
(log.f64 1)
(fabs.f64 (*.f64 2/3 x))
(pow.f64 (/.f64 3/2 x) -1)

Outputs
(/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
(/.f64 1 (+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x))))
(/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))

Calls

1 calls:

20.0ms

Results

Error	Segments	Branch
24.8b	3	`x`

Compiler

Compiled 85 to 69 computations (18.8% saved)

bsearch147.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
94.0ms	5.630164672282824e+73	1.3185189752497205e+82
53.0ms	-35735.932455582246	-0.005132707857223667

Compiler

Compiled 21 to 17 computations (19% saved)

regimes15.0ms (0.2%)

Counts

4 → 3

Calls

Call 1

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

Outputs
(/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
(/.f64 1 (/.f64 3/2 x))
(/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
25.2b	3	`x`

Compiler

Compiled 29 to 23 computations (20.7% saved)

bsearch47.0ms (0.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
46.0ms	0.20903663531356512	72.95568198013368
0.0ms	-21473740835801550.0	-20857564087258052.0

Compiler

Compiled 21 to 17 computations (19% saved)

regimes5.0ms (0.1%)

Accuracy

Total -31.9b remaining (-117.3%)

Threshold costs -31.9b (-117.3%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
27.2b	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	131
1	47	131

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)
(if (<=.f64 x -4911509158041303/137438953472) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1)) (if (<=.f64 x 56301646722828240316817350118226714903732003595341528270054161448284717056) (/.f64 1 (+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))))
(if (<=.f64 x -21000000000000000) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1)) (if (<=.f64 x 7531338503239633/36028797018963968) (/.f64 1 (/.f64 3/2 x)) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))))
(/.f64 1 (/.f64 3/2 x))
(*.f64 2/3 x)

Outputs
(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)
(if (<=.f64 x -4911509158041303/137438953472) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1)) (if (<=.f64 x 56301646722828240316817350118226714903732003595341528270054161448284717056) (/.f64 1 (+.f64 (.f64 -1/8 x) (.f64 3/2 (/.f64 1 x)))) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))))
(if (<=.f64 x -4911509158041303/137438953472) (/.f64 (.f64 x 4/3) (+.f64 1 (+.f64 1 (.f64 x 2/3)))) (if (<=.f64 x 56301646722828240316817350118226714903732003595341528270054161448284717056) (/.f64 1 (+.f64 (.f64 x -1/8) (.f64 3/2 (/.f64 1 x)))) (/.f64 (.f64 x 4/3) (+.f64 1 (+.f64 1 (.f64 x 2/3))))))
(if (<=.f64 x -21000000000000000) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1)) (if (<=.f64 x 7531338503239633/36028797018963968) (/.f64 1 (/.f64 3/2 x)) (/.f64 (.f64 x 4/3) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))))
(if (<=.f64 x -21000000000000000) (/.f64 (.f64 x 4/3) (+.f64 1 (+.f64 1 (.f64 x 2/3)))) (if (<=.f64 x 7531338503239633/36028797018963968) (/.f64 1 (/.f64 3/2 x)) (/.f64 (.f64 x 4/3) (+.f64 1 (+.f64 1 (.f64 x 2/3))))))
(/.f64 1 (/.f64 3/2 x))
(*.f64 2/3 x)
(*.f64 x 2/3)

Compiler

Compiled 95 to 77 computations (18.9% saved)

soundness13.0ms (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)

end65.0ms (0.7%)

Compiler: Compiled 91 to 73 computations (19.8% saved)