Details

analyze335.0ms (4.2%)

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (39.7%)

Results

1.5s	2090×	body	1024	valid
1.2s	5134×	body	256	valid
483.0ms	1025×	body	512	valid
8.0ms	7×	body	2048	valid

preprocess25.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune3.0ms (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

13.7b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	13.9b	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
▶	14.0b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))
✓	0.4b	(/.f64 8/3 (sin.f64 x))
✓	13.7b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 40 to 28 computations (30% saved)

series7.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

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

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

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

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

Outputs

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

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

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

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

130 → 127

Calls

Call 1

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

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

localize30.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))
✓	0.4b	(.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2)))
✓	13.7b	(/.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)))

✓

0.4b

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

✓

13.7b

(/.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 (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite83.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 109

Calls

Call 1

Inputs

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

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

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

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

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

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

145 → 138

Calls

Call 1

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

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

eval98.0ms (1.2%)

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

prune73.0ms (0.9%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	232	33	265
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	234	33	267

Error

0.0b

Counts

267 → 33

Alt Table

Click to see full alt table

Status	Error	Program
	14.0b	(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
	14.0b	(/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 2) (sin.f64 x))
	42.4b	(cbrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6))
▶	13.9b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
	24.6b	(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6)) (/.f64 8/3 (sin.f64 x)))
	30.1b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	31.9b	(pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)
	30.0b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
	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)))
▶	0.5b	(.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2)))))
	45.0b	(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
	31.7b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
▶	34.8b	(.f64 (pow.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 4) (/.f64 8/3 (sin.f64 x)))
	31.6b	(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
	0.6b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
	13.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
	45.0b	(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
	30.1b	(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
	13.9b	(/.f64 (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
	31.7b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
▶	30.0b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
	30.0b	(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
▶	31.5b	(*.f64 2/3 x)
	24.9b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
	30.0b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
	35.5b	(.f64 (exp.f64 (.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 2)) (/.f64 8/3 (sin.f64 x)))
	13.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (*.f64 (/.f64 1 (sin.f64 x)) 8/3))
	13.9b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
	45.3b	(/.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/18) 2/3))) (sin.f64 x))
	30.0b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
	30.0b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
	30.1b	(+.f64 0 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))
	44.5b	(.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))))

Compiler

Compiled 890 to 730 computations (18% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))
✓	0.2b	(.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2)))))
✓	0.2b	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
✓	0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

Compiler

Compiled 52 to 37 computations (28.8% saved)

series8.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite91.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`log-prod_binary64`
325×	`pow-prod-down_binary64`
303×	`pow2_binary64`
254×	`pow-unpow_binary64`
214×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	56
1	251	53
2	3132	48

Stop Event

1×	node limit

Counts

4 → 153

Calls

Call 1

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

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

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-l_binary64`
537×	`associate-r_binary64`
518×	`unswap-sqr_binary64`
488×	`distribute-rgt-out_binary64`
448×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	604
1	175	598
2	425	592
3	1278	592
4	3658	592
5	6194	592

Stop Event

1×	node limit

Counts

201 → 190

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)))
2
(+.f64 2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (.f64 -1/4 (pow.f64 x 2))))
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 -1/23040 (pow.f64 x 6)))))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
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 -1/18 (pow.f64 x 3) (fma.f64 1/1440 (pow.f64 x 5) (*.f64 4/3 x)))
(+.f64 (.f64 4/3 x) (+.f64 (.f64 -1/241920 (pow.f64 x 7)) (+.f64 (.f64 1/1440 (pow.f64 x 5)) (.f64 -1/18 (pow.f64 x 3)))))
(fma.f64 4/3 x (fma.f64 -1/241920 (pow.f64 x 7) (fma.f64 1/1440 (pow.f64 x 5) (*.f64 -1/18 (pow.f64 x 3)))))
(fma.f64 4/3 x (fma.f64 -1/241920 (pow.f64 x 7) (fma.f64 -1/18 (pow.f64 x 3) (*.f64 1/1440 (pow.f64 x 5)))))
(fma.f64 4/3 x (fma.f64 1/1440 (pow.f64 x 5) (fma.f64 -1/18 (pow.f64 x 3) (*.f64 -1/241920 (pow.f64 x 7)))))
(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)))))
(.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)))
2
(+.f64 2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 2 (.f64 -1/4 (.f64 x x)))
(fma.f64 -1/4 (*.f64 x x) 2)
(fma.f64 x (*.f64 x -1/4) 2)
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (.f64 -1/4 (pow.f64 x 2))))
(fma.f64 1/192 (pow.f64 x 4) (+.f64 2 (.f64 -1/4 (.f64 x x))))
(fma.f64 1/192 (pow.f64 x 4) (fma.f64 -1/4 (*.f64 x x) 2))
(fma.f64 x (*.f64 x -1/4) (fma.f64 1/192 (pow.f64 x 4) 2))
(+.f64 (.f64 1/192 (pow.f64 x 4)) (+.f64 2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 -1/23040 (pow.f64 x 6)))))
(fma.f64 1/192 (pow.f64 x 4) (+.f64 2 (fma.f64 -1/4 (.f64 x x) (.f64 -1/23040 (pow.f64 x 6)))))
(+.f64 (fma.f64 1/192 (pow.f64 x 4) (fma.f64 -1/4 (.f64 x x) 2)) (.f64 -1/23040 (pow.f64 x 6)))
(fma.f64 1/192 (pow.f64 x 4) (fma.f64 x (*.f64 x -1/4) (fma.f64 -1/23040 (pow.f64 x 6) 2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
(*.f64 2/3 x)
(*.f64 x 2/3)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 x 2/3))
(fma.f64 (pow.f64 x 3) 1/18 (*.f64 x 2/3))
(fma.f64 x 2/3 (*.f64 (pow.f64 x 3) 1/18))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 (pow.f64 x 5) 1/180)))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 x 2/3 (*.f64 (pow.f64 x 5) 1/180)))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 5) 1/180 (*.f64 (pow.f64 x 3) 1/18)))
(fma.f64 x 2/3 (fma.f64 (pow.f64 x 3) 1/18 (*.f64 (pow.f64 x 5) 1/180)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 (pow.f64 x 5) 1/180))))
(fma.f64 (pow.f64 x 3) 1/18 (fma.f64 (pow.f64 x 7) 17/30240 (fma.f64 x 2/3 (*.f64 (pow.f64 x 5) 1/180))))
(fma.f64 (pow.f64 x 7) 17/30240 (fma.f64 x 2/3 (fma.f64 (pow.f64 x 5) 1/180 (*.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 (pow.f64 x 7) 17/30240 (*.f64 x 2/3))))
(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))))
(.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 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
1/2
(+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))
(+.f64 1/2 (.f64 (.f64 x x) 1/16))
(fma.f64 (*.f64 x 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 (.f64 x x) 1/16)))
(+.f64 1/2 (fma.f64 (pow.f64 x 4) 5/768 (.f64 x (.f64 x 1/16))))
(fma.f64 (*.f64 x x) 1/16 (fma.f64 (pow.f64 x 4) 5/768 1/2))
(fma.f64 x (*.f64 x 1/16) (fma.f64 (pow.f64 x 4) 5/768 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 (.f64 x x) 1/16))))
(+.f64 1/2 (fma.f64 (pow.f64 x 6) 61/92160 (fma.f64 (pow.f64 x 4) 5/768 (.f64 x (.f64 x 1/16)))))
(fma.f64 (pow.f64 x 6) 61/92160 (fma.f64 (*.f64 x x) 1/16 (fma.f64 (pow.f64 x 4) 5/768 1/2)))
(fma.f64 (pow.f64 x 6) 61/92160 (fma.f64 x (*.f64 x 1/16) (fma.f64 (pow.f64 x 4) 5/768 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)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite48.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 2/3 x)

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

Calls

Call 1

Inputs

Outputs

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (sin.f64 x) 3/8) 2)
✓	0.2b	(*.f64 (sin.f64 x) 3/8)
✓	0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
✓	2.0b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 34 to 21 computations (38.2% saved)

series7.0ms (0.1%)

Counts

4 → 40

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.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	@	-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)

rewrite135.0ms (1.7%)

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	32
1	236	32
2	3117	27

Stop Event

1×	node limit

Counts

4 → 201

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 (neg.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2) (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (-.f64 1 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (cos.f64 x))) 2) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4)))) (sqrt.f64 (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))) (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) 2)) (/.f64 (sqrt.f64 (cos.f64 x)) (.f64 (sin.f64 x) 3/8)) (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (.f64 (sin.f64 x) 3/8))) (/.f64 (sqrt.f64 (cos.f64 x)) 2) (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (.f64 (sin.f64 x) 3/4)))) (/.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (.f64 (sin.f64 x) 3/4))) (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))))))) 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2) (sin.f64 x)) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sin.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (sin.f64 x) 3/8)) (/.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (.f64 (sin.f64 x) 3/8)) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (.f64 (sin.f64 x) 3/8)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) 2) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 x) 3/4)) -2) (/.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (pow.f64 (cbrt.f64 (.f64 (sin.f64 x) 3/4)) 2)) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (.f64 (sin.f64 x) 3/4)) 2)) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (sin.f64 x) 3/4) -1/2) (/.f64 (-.f64 1 (cos.f64 x)) (sqrt.f64 (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (sqrt.f64 (.f64 (sin.f64 x) 3/4))) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (.f64 (sin.f64 x) 3/4) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 (sin.f64 x) -3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) (pow.f64 (.f64 (sin.f64 x) 3/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1/2 (.f64 (sin.f64 x) 3/8)) (neg.f64 (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (.f64 (sin.f64 x) 3/8))) 2) (cbrt.f64 (/.f64 1/2 (.f64 (sin.f64 x) 3/8))) (neg.f64 (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 1/2 (.f64 (sin.f64 x) 3/8))) (sqrt.f64 (/.f64 1/2 (.f64 (sin.f64 x) 3/8))) (neg.f64 (/.f64 (cos.f64 x) (.f64 (sin.f64 x) 3/4))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (sin.f64 x) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/8)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/8))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 x) 3/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sin.f64 x) 3/8) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 9/64 (pow.f64 (sin.f64 x) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sin.f64 x) 3/8) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sin.f64 x) 3/8)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sin.f64 x) 3/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 9/64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 x) 3/8))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sin.f64 x) 3/8) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sin.f64 x) 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sin.f64 x) 3/8)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 (sin.f64 x) 3/8))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sin.f64 x) 3/8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sin.f64 x) 3/8))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sin.f64 x) 3/8) (.f64 (sin.f64 x) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (sin.f64 x) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/4)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/4))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 x) 3/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sin.f64 x) 3/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (sin.f64 x) 2) 9/16) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sin.f64 x) 3/4) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sin.f64 x) 3/4)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sin.f64 x) 3/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (sin.f64 x) 2) 9/16))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sin.f64 x)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sin.f64 x) 3/4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sin.f64 x) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (sin.f64 x) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sin.f64 x) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sin.f64 x) 3/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 (sin.f64 x) 3/4))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sin.f64 x) 3/4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sin.f64 x) 3/4))) 2))))))

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

837×	`distribute-rgt-out_binary64`
739×	`associate-r_binary64`
692×	`unswap-sqr_binary64`
579×	`distribute-lft-in_binary64`
387×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	412
1	193	412
2	469	412
3	1447	412
4	3257	412
5	6085	412
6	7345	412

Stop Event

1×	node limit

Counts

241 → 239

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))
(*.f64 3/4 x)
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (.f64 3/4 x))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 3/4 x) (*.f64 1/160 (pow.f64 x 5))))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/6720 (pow.f64 x 7)) (+.f64 (.f64 3/4 x) (.f64 1/160 (pow.f64 x 5)))))
(*.f64 3/4 (sin.f64 x))
(*.f64 3/4 (sin.f64 x))
(*.f64 3/4 (sin.f64 x))
(*.f64 3/4 (sin.f64 x))
(*.f64 3/4 (sin.f64 x))
(*.f64 3/4 (sin.f64 x))
(*.f64 3/4 (sin.f64 x))
(*.f64 3/4 (sin.f64 x))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/24 (pow.f64 x 4))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (.f64 1/2 (.f64 x x))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (.f64 -1/40320 (pow.f64 x 8)))))
(*.f64 2/3 x)
(*.f64 x 2/3)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 x 2/3))
(fma.f64 x 2/3 (*.f64 1/18 (pow.f64 x 3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 x 2/3 (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 x 2/3 (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 x 2/3 (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 x 2/3 (fma.f64 17/30240 (pow.f64 x 7) (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 x 2/3 (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
(*.f64 4/3 (tan.f64 (/.f64 x 2)))
(*.f64 3/8 x)
(*.f64 x 3/8)
(+.f64 (.f64 -1/16 (pow.f64 x 3)) (.f64 3/8 x))
(fma.f64 -1/16 (pow.f64 x 3) (*.f64 x 3/8))
(fma.f64 (pow.f64 x 3) -1/16 (*.f64 x 3/8))
(fma.f64 x 3/8 (*.f64 (pow.f64 x 3) -1/16))
(+.f64 (.f64 1/320 (pow.f64 x 5)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (*.f64 3/8 x)))
(fma.f64 1/320 (pow.f64 x 5) (fma.f64 -1/16 (pow.f64 x 3) (*.f64 x 3/8)))
(fma.f64 (pow.f64 x 5) 1/320 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 x 3/8)))
(fma.f64 (pow.f64 x 3) -1/16 (fma.f64 x 3/8 (*.f64 (pow.f64 x 5) 1/320)))
(fma.f64 x 3/8 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 (pow.f64 x 5) 1/320)))
(+.f64 (.f64 1/320 (pow.f64 x 5)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (+.f64 (.f64 -1/13440 (pow.f64 x 7)) (.f64 3/8 x))))
(fma.f64 1/320 (pow.f64 x 5) (fma.f64 -1/16 (pow.f64 x 3) (fma.f64 -1/13440 (pow.f64 x 7) (*.f64 x 3/8))))
(fma.f64 (pow.f64 x 5) 1/320 (fma.f64 (pow.f64 x 3) -1/16 (fma.f64 (pow.f64 x 7) -1/13440 (*.f64 x 3/8))))
(fma.f64 (pow.f64 x 5) 1/320 (fma.f64 (pow.f64 x 7) -1/13440 (fma.f64 x 3/8 (*.f64 (pow.f64 x 3) -1/16))))
(fma.f64 (pow.f64 x 3) -1/16 (fma.f64 (pow.f64 x 5) 1/320 (fma.f64 x 3/8 (*.f64 (pow.f64 x 7) -1/13440))))
(*.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)
(*.f64 3/4 x)
(*.f64 x 3/4)
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (.f64 3/4 x))
(fma.f64 -1/8 (pow.f64 x 3) (*.f64 x 3/4))
(fma.f64 (pow.f64 x 3) -1/8 (*.f64 x 3/4))
(fma.f64 x 3/4 (*.f64 (pow.f64 x 3) -1/8))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 3/4 x) (*.f64 1/160 (pow.f64 x 5))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 3/4 x (*.f64 (pow.f64 x 5) 1/160)))
(fma.f64 (pow.f64 x 3) -1/8 (fma.f64 (pow.f64 x 5) 1/160 (*.f64 x 3/4)))
(fma.f64 x 3/4 (fma.f64 (pow.f64 x 3) -1/8 (*.f64 (pow.f64 x 5) 1/160)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/6720 (pow.f64 x 7)) (+.f64 (.f64 3/4 x) (.f64 1/160 (pow.f64 x 5)))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/6720 (pow.f64 x 7) (fma.f64 3/4 x (*.f64 (pow.f64 x 5) 1/160))))
(fma.f64 (pow.f64 x 3) -1/8 (fma.f64 (pow.f64 x 7) -1/6720 (fma.f64 (pow.f64 x 5) 1/160 (*.f64 x 3/4))))
(fma.f64 (pow.f64 x 3) -1/8 (fma.f64 (pow.f64 x 5) 1/160 (fma.f64 x 3/4 (*.f64 (pow.f64 x 7) -1/6720))))
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)
(*.f64 3/4 (sin.f64 x))
(*.f64 (sin.f64 x) 3/4)

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
✓	0.3b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
✓	13.6b	(/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x))

Compiler

Compiled 40 to 29 computations (27.5% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

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

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

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

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

152 → 145

Calls

Call 1

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

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

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
	0.4b	(/.f64 8/3 (sin.f64 x))
✓	0.4b	(pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 4)
✓	7.1b	(.f64 (pow.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 4) (/.f64 8/3 (sin.f64 x)))

Compiler

Compiled 42 to 31 computations (26.2% saved)

series6.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 4)
1.0ms	x	@	0	(pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 4)
1.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 4)
0.0ms	x	@	0	(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
0.0ms	x	@	0	(.f64 (pow.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 4) (/.f64 8/3 (sin.f64 x)))

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

515×	`log-prod_binary64`
391×	`exp-prod_binary64`
293×	`pow2_binary64`
286×	`pow-prod-down_binary64`
204×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	254	34
2	2886	34

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

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

simplify121.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	330
1	74	330
2	161	330
3	403	330
4	788	330
5	1949	330
6	3586	330
7	5348	330
8	6255	330
9	6629	330
10	7101	330
11	7830	330

Stop Event

1×	node limit

Counts

130 → 115

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)))
(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)
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (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 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 x (fma.f64 x (.f64 x 1/18) 2/3) (.f64 1/180 (pow.f64 x 5)))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 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 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(fma.f64 1/180 (pow.f64 x 5) (fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 2/3 x))))
(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 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(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)
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))
(sqrt.f64 (sin.f64 (*.f64 1/2 x)))
(sqrt.f64 (sin.f64 (*.f64 x 1/2)))

eval338.0ms (4.2%)

Compiler: Compiled 14560 to 10357 computations (28.9% saved)

prune123.0ms (1.5%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	735	17	752
Fresh	27	1	28
Picked	0	1	1
Done	2	2	4
Total	764	21	785

Error

Counts

785 → 21

Alt Table

Click to see full alt table

Status	Error	Program
✓	13.9b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
▶	1.1b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
	0.5b	(/.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (/.f64 1 (sin.f64 (*.f64 x 1/2))))
	31.6b	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
	60.0b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
▶	0.2b	(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
	19.4b	(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))
	44.9b	(fabs.f64 (*.f64 2/3 x))
	29.3b	(log.f64 (exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
	30.0b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
	31.6b	(.f64 8/3 (+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (.f64 1/4 x))))
▶	0.3b	(pow.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) -1)
▶	0.3b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
	31.8b	(pow.f64 (sqrt.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) 2)
	40.2b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))) 1)
	60.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
✓	34.8b	(.f64 (pow.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 4) (/.f64 8/3 (sin.f64 x)))
	30.0b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/4))
✓	31.5b	(*.f64 2/3 x)
	30.0b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
▶	31.5b	(.f64 8/3 (.f64 1/4 x))

Compiler

Compiled 415 to 352 computations (15.2% saved)

localize16.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 26 to 21 computations (19.2% saved)

series6.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	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)

rewrite60.0ms (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)))))))

simplify165.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

35 → 32

Calls

Call 1

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

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 8/3 (.f64 1/4 x))

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite48.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

524×	`pow1_binary64`
515×	`add-sqr-sqrt_binary64`
492×	`add-log-exp_binary64`
492×	`log1p-expm1-u_binary64`
492×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	125	4
2	1342	4

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 8/3 (.f64 1/4 x))

Outputs

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

simplify10.0ms (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

23 → 12

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)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.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 (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 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)))))))))

simplify166.0ms (2.1%)

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))))

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 37 to 31 computations (16.2% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite68.0ms (0.8%)

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

Outputs

((#(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)))))))

((#(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)))))))))

simplify152.0ms (1.9%)

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

88 → 82

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))))

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (tan.f64 (/.f64 x 2)) 3/4)
✓	0.2b	(expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
✓	0.8b	(log1p.f64 (expm1.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	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
0.0ms	x	@	0	(expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
0.0ms	x	@	inf	(expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
0.0ms	x	@	-inf	(expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
0.0ms	x	@	-inf	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

813×	`pow1_binary64`
765×	`expm1-log1p-u_binary64`
764×	`add-log-exp_binary64`
764×	`log1p-expm1-u_binary64`
752×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	181	20
2	2077	20

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
(expm1.f64 (/.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 /.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 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 exp.f64 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)))))))

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

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

590×	`distribute-lft-out_binary64`
511×	`fma-def_binary64`
385×	`distribute-rgt-in_binary64`
362×	`associate-/l*_binary64`
334×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	404
1	115	404
2	261	401
3	768	393
4	2111	393
5	3399	393
6	4235	393
7	5476	393
8	7862	393

Stop Event

1×	node limit

Counts

74 → 67

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 2/3 x)
(+.f64 (.f64 2/3 x) (.f64 2/9 (pow.f64 x 2)))
(+.f64 (.f64 17/162 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 2/9 (pow.f64 x 2))))
(+.f64 (.f64 17/162 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (+.f64 (.f64 2/9 (pow.f64 x 2)) (.f64 11/243 (pow.f64 x 4)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 2/3 x (*.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))))
(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 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 2/3 x)
(+.f64 (.f64 2/3 x) (.f64 2/9 (pow.f64 x 2)))
(fma.f64 2/3 x (.f64 2/9 (.f64 x x)))
(.f64 x (+.f64 2/3 (.f64 x 2/9)))
(*.f64 x (fma.f64 x 2/9 2/3))
(+.f64 (.f64 17/162 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 2/9 (pow.f64 x 2))))
(fma.f64 17/162 (pow.f64 x 3) (fma.f64 2/3 x (.f64 2/9 (.f64 x x))))
(fma.f64 (pow.f64 x 3) 17/162 (fma.f64 2/3 x (.f64 2/9 (.f64 x x))))
(fma.f64 (pow.f64 x 3) 17/162 (.f64 x (+.f64 2/3 (.f64 x 2/9))))
(.f64 x (+.f64 2/3 (.f64 x (fma.f64 x 17/162 2/9))))
(+.f64 (.f64 17/162 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (+.f64 (.f64 2/9 (pow.f64 x 2)) (.f64 11/243 (pow.f64 x 4)))))
(fma.f64 17/162 (pow.f64 x 3) (fma.f64 2/3 x (fma.f64 2/9 (.f64 x x) (.f64 11/243 (pow.f64 x 4)))))
(fma.f64 (pow.f64 x 3) 17/162 (fma.f64 2/3 x (fma.f64 11/243 (pow.f64 x 4) (.f64 2/9 (.f64 x x)))))
(fma.f64 (pow.f64 x 3) 17/162 (fma.f64 11/243 (pow.f64 x 4) (.f64 x (+.f64 2/3 (.f64 x 2/9)))))
(fma.f64 x (fma.f64 x 2/9 2/3) (.f64 (pow.f64 x 3) (+.f64 (.f64 x 11/243) 17/162)))
(fma.f64 x (fma.f64 x 2/9 2/3) (.f64 (pow.f64 x 3) (+.f64 17/162 (.f64 x 11/243))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))) 1)
(expm1.f64 (.f64 4/3 (/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))

eval95.0ms (1.2%)

Compiler: Compiled 3307 to 2842 computations (14.1% saved)

prune54.0ms (0.7%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	268	11	279
Fresh	8	5	13
Picked	1	0	1
Done	4	3	7
Total	281	19	300

Error

Counts

300 → 19

Alt Table

Click to see full alt table

Status	Error	Program
	31.5b	(pow.f64 (/.f64 3/2 x) -1)
▶	19.4b	(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))
✓	31.5b	(*.f64 2/3 x)
	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/4 (cos.f64 (*.f64 x 1/2))))
	29.2b	(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
✓	0.3b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
	0.4b	(pow.f64 (.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 3/4) -1)
	30.0b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
	0.4b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))
▶	60.0b	(-.f64 (+.f64 1 (*.f64 x 2/3)) 1)
✓	31.5b	(.f64 8/3 (.f64 1/4 x))
	0.3b	(/.f64 1 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))
	60.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
	31.9b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 3/4 (tan.f64 (*.f64 x 1/2)))) 2) -1)
	44.9b	(fabs.f64 (*.f64 2/3 x))
▶	30.0b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/4))
	0.4b	(pow.f64 (.f64 (/.f64 3/4 (sin.f64 (.f64 x 1/2))) (cos.f64 (*.f64 x 1/2))) -1)
▶	31.6b	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
▶	0.2b	(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)

Compiler

Compiled 353 to 300 computations (15% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.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)

rewrite53.0ms (0.7%)

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)))))))

simplify162.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

35 → 32

Calls

Call 1

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

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

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite64.0ms (0.8%)

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	20
1	156	8
2	2109	8

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 x 2/3 -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 x 2/3 -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 2/3) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 2/3 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 x 2/3 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 2/3 -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 x 2/3 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 x 2/3 1) 3) (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) (+.f64 (*.f64 x 2/3) 2))) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) (+.f64 (*.f64 x 2/3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 x 2/3 1) 2) (+.f64 (*.f64 x 2/3) 2)) (/.f64 1 (+.f64 (*.f64 x 2/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) (+.f64 (*.f64 x 2/3) 2)) (+.f64 (pow.f64 (fma.f64 x 2/3 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 x 2/3) 2) (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 3) -1) (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) (+.f64 (*.f64 x 2/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 3) -1) (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) (-.f64 1 (*.f64 (fma.f64 x 2/3 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) -1) (+.f64 (*.f64 x 2/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) -1) (-.f64 (fma.f64 x 2/3 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) (+.f64 (*.f64 x 2/3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x 2/3 1) 2) -1)) (neg.f64 (+.f64 (*.f64 x 2/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 x 2/3 -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 x 2/3 -1) (fma.f64 x 2/3 -1)) (fma.f64 x 2/3 -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 x 2/3 -1) (fma.f64 x 2/3 -1))) (-.f64 1 (fma.f64 x 2/3 -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 2/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 2/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 8/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x 2/3) 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 (pow.f64 x 3) 8/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 2/3 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 2/3 1)) 2) (cbrt.f64 (fma.f64 x 2/3 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 2/3 1)) (sqrt.f64 (fma.f64 x 2/3 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	96
1	5	96

Stop Event

1×

saturated

Counts

99 → 46

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

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (*.f64 x 1/18) 2/3)
✓	0.2b	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
✓	0.4b	(*.f64 x 1/18)

Compiler

Compiled 21 to 14 computations (33.3% saved)

series9.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
1.0ms	x	@	-inf	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
1.0ms	x	@	inf	(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
1.0ms	x	@	0	(*.f64 x 1/18)
0.0ms	x	@	-inf	(*.f64 x 1/18)

rewrite64.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`pow1_binary64`
596×	`add-log-exp_binary64`
596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
585×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
1	142	23
2	1592	23

Stop Event

1×	node limit

Counts

3 → 45

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/18)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/18) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 1/18) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/18)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/18)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/324 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 1/18))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 1/18) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/18)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/18)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/18)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 1/18)) x) (*.f64 2/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x (*.f64 x 1/18))) (*.f64 x 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 x (*.f64 x 1/18) 2/3)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x (*.f64 x 1/18) 2/3))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 2/3 (*.f64 x (*.f64 x 1/18)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 1/18)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 1/18)) 1) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (*.f64 x 1/18) 2/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x 1/18) 2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x 1/18) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)) 2) (cbrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)) (sqrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/18)) 3) 8/27) (+.f64 (*.f64 (*.f64 x (*.f64 x 1/18)) (*.f64 x (*.f64 x 1/18))) (-.f64 4/9 (*.f64 (*.f64 x (*.f64 x 1/18)) 2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 1/18)) (*.f64 x (*.f64 x 1/18))) 4/9) (-.f64 (*.f64 x (*.f64 x 1/18)) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x 1/18) 2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 1/18) 2/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x 1/18) 2/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x 1/18) 2/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x 1/18) 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 1/18) 2/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x 1/18) 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x 1/18) 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x 1/18) 2/3)))))))

simplify186.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

944×	`sqr-pow_binary64`
564×	`cube-prod_binary64`
536×	`unswap-sqr_binary64`
532×	`fabs-mul_binary64`
414×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	270
1	33	252
2	61	252
3	125	252
4	359	252
5	1398	252
6	2776	252
7	2962	252
8	3212	252
9	3499	252
10	3878	252
11	4389	252
12	4996	252
13	5706	252
14	6177	252
15	6494	252
16	6764	252
17	6932	252
18	7026	252
19	7703	252

Stop Event

1×	node limit

Counts

81 → 56

Calls

Call 1

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

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

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 x) 3/4)
✓	0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/4))
	2.0b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 25 to 14 computations (44% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite89.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	192	15
2	2602	15

Stop Event

1×	node limit

Counts

2 → 132

Calls

Call 1

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

Outputs

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

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

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-def_binary64`
624×	`unswap-sqr_binary64`
520×	`associate-l_binary64`
495×	`sqr-pow_binary64`
351×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	236
1	109	236
2	255	236
3	681	236
4	1240	236
5	2615	236
6	3771	236
7	5043	236
8	5553	236
9	6073	236
10	6537	236
11	7178	236

Stop Event

1×	node limit

Counts

156 → 150

Calls

Call 1

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

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

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (tan.f64 (/.f64 x 2)) 3/4)
✓	0.5b	(pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3)
✓	19.4b	(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))

Compiler

Compiled 35 to 29 computations (17.1% saved)

series6.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite72.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

902×	`pow1_binary64`
858×	`add-log-exp_binary64`
857×	`log1p-expm1-u_binary64`
857×	`expm1-log1p-u_binary64`
842×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	229	21
2	2419	21

Stop Event

1×	node limit

Counts

2 → 69

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (pow.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 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) (pow.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) 1/3))))) (#(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 (pow.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) 1/3) (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) 3/2) 1/3) (pow.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) 3/2) 1/3))))) (#(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 (cbrt.f64 (pow.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 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27) 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 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 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 4/3 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 2) (*.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) (*.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) 3/2) (pow.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 2) 3) (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 3) (pow.f64 (sqrt.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) (tan.f64 (*.f64 x 1/2))) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) 1) (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) (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 (*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) (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 (pow.f64 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 27/64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 27/64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) 3) -27/64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)) -27/64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9)) 3/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9)) -3/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) (tan.f64 (*.f64 x 1/2))) 3/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) 1) (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 16/9) (neg.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) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 64/27)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 (*.f64 (tan.f64 (*.f64 x 1/2)) 4/3))))))))

simplify122.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1444×	`fma-def_binary64`
821×	`unswap-sqr_binary64`
636×	`associate-/r/_binary64`
335×	`associate-l_binary64`
287×	`associate-r_binary64`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	51	514
1	139	504
2	399	488
3	1312	462
4	4079	462
5	5147	462
6	5583	462
7	6871	462
8	7086	462
9	7392	460

Stop Event

1×	node limit

Counts

93 → 89

Calls

Call 1

Inputs
(.f64 1/2 (.f64 x (cbrt.f64 64/27)))
(+.f64 (.f64 1/24 (.f64 (pow.f64 x 3) (cbrt.f64 64/27))) (.f64 1/2 (.f64 x (cbrt.f64 64/27))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 x 3) (cbrt.f64 64/27))) (+.f64 (.f64 1/240 (.f64 (pow.f64 x 5) (cbrt.f64 64/27))) (.f64 1/2 (.f64 x (cbrt.f64 64/27)))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 x 3) (cbrt.f64 64/27))) (+.f64 (.f64 17/40320 (.f64 (pow.f64 x 7) (cbrt.f64 64/27))) (+.f64 (.f64 1/240 (.f64 (pow.f64 x 5) (cbrt.f64 64/27))) (.f64 1/2 (.f64 x (cbrt.f64 64/27))))))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(*.f64 8/27 (pow.f64 x 3))
(+.f64 (.f64 2/27 (pow.f64 x 5)) (.f64 8/27 (pow.f64 x 3)))
(+.f64 (.f64 2/27 (pow.f64 x 5)) (+.f64 (.f64 11/810 (pow.f64 x 7)) (*.f64 8/27 (pow.f64 x 3))))
(+.f64 (.f64 2/27 (pow.f64 x 5)) (+.f64 (.f64 11/5103 (pow.f64 x 9)) (+.f64 (.f64 11/810 (pow.f64 x 7)) (.f64 8/27 (pow.f64 x 3)))))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))

Outputs
(.f64 1/2 (.f64 x (cbrt.f64 64/27)))
(.f64 (cbrt.f64 64/27) (.f64 1/2 x))
(+.f64 (.f64 1/24 (.f64 (pow.f64 x 3) (cbrt.f64 64/27))) (.f64 1/2 (.f64 x (cbrt.f64 64/27))))
(fma.f64 1/24 (.f64 (cbrt.f64 64/27) (pow.f64 x 3)) (.f64 1/2 (*.f64 x (cbrt.f64 64/27))))
(.f64 (cbrt.f64 64/27) (+.f64 (.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))
(.f64 (cbrt.f64 64/27) (fma.f64 1/2 x (.f64 1/24 (pow.f64 x 3))))
(.f64 (cbrt.f64 64/27) (.f64 x (fma.f64 1/24 (*.f64 x x) 1/2)))
(+.f64 (.f64 1/24 (.f64 (pow.f64 x 3) (cbrt.f64 64/27))) (+.f64 (.f64 1/240 (.f64 (pow.f64 x 5) (cbrt.f64 64/27))) (.f64 1/2 (.f64 x (cbrt.f64 64/27)))))
(fma.f64 1/24 (.f64 (cbrt.f64 64/27) (pow.f64 x 3)) (fma.f64 1/240 (.f64 (cbrt.f64 64/27) (pow.f64 x 5)) (.f64 1/2 (.f64 x (cbrt.f64 64/27)))))
(fma.f64 1/24 (.f64 (cbrt.f64 64/27) (pow.f64 x 3)) (.f64 (cbrt.f64 64/27) (+.f64 (.f64 1/2 x) (.f64 1/240 (pow.f64 x 5)))))
(.f64 (cbrt.f64 64/27) (+.f64 (.f64 1/2 x) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5)))))
(.f64 (cbrt.f64 64/27) (fma.f64 x (fma.f64 1/24 (.f64 x x) 1/2) (*.f64 1/240 (pow.f64 x 5))))
(.f64 (cbrt.f64 64/27) (fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (.f64 1/240 (pow.f64 x 5)))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 x 3) (cbrt.f64 64/27))) (+.f64 (.f64 17/40320 (.f64 (pow.f64 x 7) (cbrt.f64 64/27))) (+.f64 (.f64 1/240 (.f64 (pow.f64 x 5) (cbrt.f64 64/27))) (.f64 1/2 (.f64 x (cbrt.f64 64/27))))))
(fma.f64 1/24 (.f64 (cbrt.f64 64/27) (pow.f64 x 3)) (fma.f64 17/40320 (.f64 (cbrt.f64 64/27) (pow.f64 x 7)) (fma.f64 1/240 (.f64 (cbrt.f64 64/27) (pow.f64 x 5)) (.f64 1/2 (*.f64 x (cbrt.f64 64/27))))))
(+.f64 (.f64 (cbrt.f64 64/27) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/240 (pow.f64 x 5)))) (.f64 (cbrt.f64 64/27) (+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))))
(.f64 (cbrt.f64 64/27) (+.f64 (fma.f64 1/2 x (.f64 1/240 (pow.f64 x 5))) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(.f64 (cbrt.f64 64/27) (+.f64 (.f64 1/24 (pow.f64 x 3)) (fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 17/40320 (pow.f64 x 7))))))
(.f64 (cbrt.f64 64/27) (+.f64 (.f64 1/24 (pow.f64 x 3)) (fma.f64 1/2 x (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/240 (pow.f64 x 5))))))
(.f64 (cbrt.f64 64/27) (fma.f64 x (fma.f64 1/24 (.f64 x x) 1/2) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/240 (pow.f64 x 5)))))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (cos.f64 (.f64 1/2 x)) (cbrt.f64 64/27)))
(/.f64 (cbrt.f64 64/27) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (.f64 (cbrt.f64 64/27) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 8/27 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) 8/27)
(+.f64 (.f64 2/27 (pow.f64 x 5)) (.f64 8/27 (pow.f64 x 3)))
(fma.f64 2/27 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 8/27))
(fma.f64 (pow.f64 x 3) 8/27 (*.f64 (pow.f64 x 5) 2/27))
(+.f64 (.f64 2/27 (pow.f64 x 5)) (+.f64 (.f64 11/810 (pow.f64 x 7)) (*.f64 8/27 (pow.f64 x 3))))
(fma.f64 2/27 (pow.f64 x 5) (fma.f64 11/810 (pow.f64 x 7) (*.f64 (pow.f64 x 3) 8/27)))
(fma.f64 (pow.f64 x 5) 2/27 (fma.f64 (pow.f64 x 3) 8/27 (*.f64 (pow.f64 x 7) 11/810)))
(fma.f64 (pow.f64 x 3) 8/27 (fma.f64 (pow.f64 x 5) 2/27 (*.f64 (pow.f64 x 7) 11/810)))
(+.f64 (.f64 2/27 (pow.f64 x 5)) (+.f64 (.f64 11/5103 (pow.f64 x 9)) (+.f64 (.f64 11/810 (pow.f64 x 7)) (.f64 8/27 (pow.f64 x 3)))))
(fma.f64 2/27 (pow.f64 x 5) (fma.f64 11/5103 (pow.f64 x 9) (fma.f64 11/810 (pow.f64 x 7) (*.f64 (pow.f64 x 3) 8/27))))
(fma.f64 (pow.f64 x 5) 2/27 (fma.f64 11/5103 (pow.f64 x 9) (fma.f64 (pow.f64 x 3) 8/27 (*.f64 (pow.f64 x 7) 11/810))))
(fma.f64 (pow.f64 x 5) 2/27 (fma.f64 (pow.f64 x 3) 8/27 (fma.f64 (pow.f64 x 7) 11/810 (*.f64 11/5103 (pow.f64 x 9)))))
(fma.f64 (pow.f64 x 7) 11/810 (fma.f64 (pow.f64 x 3) 8/27 (fma.f64 (pow.f64 x 5) 2/27 (*.f64 11/5103 (pow.f64 x 9)))))
(fma.f64 (pow.f64 x 3) 8/27 (fma.f64 (pow.f64 x 5) 2/27 (fma.f64 (pow.f64 x 7) 11/810 (*.f64 11/5103 (pow.f64 x 9)))))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))
(.f64 64/27 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(.f64 64/27 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) 3))
(/.f64 64/27 (pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))) 3))

eval189.0ms (2.3%)

Compiler: Compiled 7823 to 5502 computations (29.7% saved)

prune74.0ms (0.9%)

Pruning

19 alts after pruning (12 fresh and 7 done)

	Pruned	Kept	Total
New	454	6	460
Fresh	5	6	11
Picked	0	1	1
Done	1	6	7
Total	460	19	479

Error

Counts

479 → 19

Alt Table

Click to see full alt table

Status	Error	Program
	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/4 (cos.f64 (*.f64 x 1/2))))
	0.8b	(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
	31.5b	(pow.f64 (/.f64 3/2 x) -1)
✓	19.4b	(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4) 3))
	30.0b	(*.f64 (/.f64 4/3 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
✓	30.0b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/4))
✓	31.5b	(*.f64 2/3 x)
	31.7b	(+.f64 (.f64 (.f64 x (.f64 x 1/18)) x) (.f64 2/3 x))
✓	0.3b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
	31.6b	(.f64 x (+.f64 (.f64 x (*.f64 x 1/18)) 2/3))
	0.4b	(pow.f64 (.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 3/4) -1)
✓	60.0b	(-.f64 (+.f64 1 (*.f64 x 2/3)) 1)
✓	31.5b	(.f64 8/3 (.f64 1/4 x))
	0.3b	(/.f64 1 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))
	60.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 2/3 x)) (+.f64 1 (.f64 2/3 x))) 1) (+.f64 (+.f64 1 (.f64 2/3 x)) 1))
	29.2b	(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
	44.9b	(fabs.f64 (*.f64 2/3 x))
	0.4b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 4/3) (cos.f64 (*.f64 x 1/2)))
✓	0.2b	(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)

Compiler

Compiled 185 to 154 computations (16.8% saved)

regimes94.0ms (1.2%)

Counts

69 → 1

Calls

Call 1

Inputs
(*.f64 2/3 x)
(.f64 8/3 (.f64 1/4 x))
(-.f64 (+.f64 1 (*.f64 x 2/3)) 1)
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(.f64 x (+.f64 (.f64 x (*.f64 x 1/18)) 2/3))
(+.f64 (.f64 (.f64 x (.f64 x 1/18)) x) (.f64 2/3 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))
(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 1 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(.f64 x (fma.f64 x (.f64 x 1/18) 2/3))
(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
(.f64 x (fma.f64 1/18 (.f64 x x) 2/3))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
(-.f64 (+.f64 1 (.f64 (tan.f64 (.f64 x 1/2)) 4/3)) 1)
(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
(*.f64 (/.f64 4/3 (sin.f64 x)) (-.f64 1 (cos.f64 x)))
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) 3/4))
(*.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)
(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 (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 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) (/.f64 1 (sin.f64 x))))
(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
(/.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/18) 2/3))) (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 8/3 (+.f64 (.f64 1/48 (pow.f64 x 3)) (+.f64 (.f64 1/480 (pow.f64 x 5)) (.f64 1/4 x))))
(.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))))
(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
(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 (sqrt.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) 2)
(-.f64 (exp.f64 (log1p.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))) 1)
(.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (/.f64 8/3 (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 64/27)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (.f64 (/.f64 3/4 (sin.f64 (.f64 x 1/2))) (cos.f64 (*.f64 x 1/2))) -1)
(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 (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))) (sin.f64 x)) (/.f64 1 (sin.f64 (*.f64 x 1/2))))
(.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 1 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2)))))
(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (*.f64 (/.f64 1 (sin.f64 x)) 8/3))
(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 3/4 (tan.f64 (*.f64 x 1/2)))) 2) -1)
(/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 2) (sin.f64 x))
(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6)) (/.f64 8/3 (sin.f64 x)))
(pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 2)
(.f64 (pow.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 4) (/.f64 8/3 (sin.f64 x)))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
(.f64 (exp.f64 (.f64 (log.f64 (sin.f64 (*.f64 x 1/2))) 2)) (/.f64 8/3 (sin.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (/.f64 8/3 (sin.f64 x)))) 6))
(.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)))

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

Calls

2 calls:

36.0ms	x
29.0ms	(/.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
0.2b	1	`x`
0.2b	1	`(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))`

Compiler

Compiled 788 to 596 computations (24.4% saved)

regimes11.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 2/3 x)
(.f64 8/3 (.f64 1/4 x))
(-.f64 (+.f64 1 (*.f64 x 2/3)) 1)
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(.f64 x (+.f64 (.f64 x (*.f64 x 1/18)) 2/3))
(+.f64 (.f64 (.f64 x (.f64 x 1/18)) x) (.f64 2/3 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))
(fabs.f64 (*.f64 2/3 x))
(pow.f64 (/.f64 3/2 x) -1)

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
31.5b	1	`x`

Compiler

Compiled 75 to 58 computations (22.7% saved)

regimes9.0ms (0.1%)

Accuracy

Total -30.1b remaining (-95.7%)

Threshold costs -30.1b (-95.7%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 2/3 x)
(.f64 8/3 (.f64 1/4 x))
(-.f64 (+.f64 1 (*.f64 x 2/3)) 1)
(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
(.f64 x (+.f64 (.f64 x (*.f64 x 1/18)) 2/3))
(+.f64 (.f64 (.f64 x (.f64 x 1/18)) x) (.f64 2/3 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))
(fabs.f64 (*.f64 2/3 x))

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

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
31.5b	1	`x`

Compiler

Compiled 70 to 54 computations (22.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	21	27

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

Outputs
(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)
(pow.f64 (/.f64 3/2 x) -1)
(.f64 8/3 (.f64 1/4 x))
(.f64 8/3 (.f64 x 1/4))
(*.f64 2/3 x)
(*.f64 x 2/3)

Compiler

Compiled 23 to 19 computations (17.4% saved)

soundness13.0ms (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

Compiler

Compiled 83 to 68 computations (18.1% saved)

end33.0ms (0.4%)

Compiler: Compiled 20 to 16 computations (20% saved)