Details

analyze417.0ms (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)

sample4.3s (43%)

Results

2.0s	2126×	body	1024	valid
1.7s	5143×	body	256	valid
500.0ms	982×	body	512	valid
6.0ms	5×	body	2048	valid

preprocess26.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

14.7b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.8b	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
▶	14.9b	(.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)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 (*.f64 x 1/2))
✓	0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (*.f64 x 1/2)))
✓	0.4b	(/.f64 8/3 (sin.f64 x))
✓	14.7b	(.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)

series11.0ms (0.1%)

Counts

4 → 40

Calls

12 calls:

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

rewrite87.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	220	38
2	2873	38

Stop Event

1×	node limit

Counts

4 → 134

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

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

930×	`distribute-rgt-out_binary64`
731×	`associate-r_binary64`
702×	`unswap-sqr_binary64`
670×	`distribute-lft-in_binary64`
326×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	491
1	177	491
2	437	491
3	1330	491
4	3080	491
5	6225	491

Stop Event

1×	node limit

Counts

174 → 169

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)
(*.f64 1/2 x)
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (.f64 1/2 x))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 1/2 x) (*.f64 1/3840 (pow.f64 x 5))))
(+.f64 (.f64 -1/645120 (pow.f64 x 7)) (+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 1/2 x) (.f64 1/3840 (pow.f64 x 5)))))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.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 (.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 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)))
(+.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 (pow.f64 x 3) 7/135 (fma.f64 (pow.f64 x 5) 31/5670 (/.f64 8/3 x))))
(*.f64 1/4 (pow.f64 x 2))
(.f64 1/4 (.f64 x x))
(.f64 (.f64 1/4 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 -1/48 (pow.f64 x 4) (.f64 (.f64 1/4 x) x))
(fma.f64 x (.f64 x 1/4) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 -1/48 (pow.f64 x 4) (.f64 1/4 (.f64 x x)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 x (.f64 x 1/4) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6))))
(fma.f64 -1/48 (pow.f64 x 4) (fma.f64 1/1440 (pow.f64 x 6) (.f64 1/4 (.f64 x x))))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 x (.f64 x 1/4) (fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 -1/48 (pow.f64 x 4) (.f64 1/1440 (pow.f64 x 6)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 -1/48 (pow.f64 x 4) (fma.f64 1/1440 (pow.f64 x 6) (.f64 1/4 (.f64 x x)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(*.f64 1/2 x)
(*.f64 x 1/2)
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (.f64 1/2 x))
(fma.f64 -1/48 (pow.f64 x 3) (*.f64 x 1/2))
(fma.f64 (pow.f64 x 3) -1/48 (*.f64 x 1/2))
(fma.f64 x 1/2 (*.f64 (pow.f64 x 3) -1/48))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 1/2 x) (*.f64 1/3840 (pow.f64 x 5))))
(fma.f64 -1/48 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (pow.f64 x 5) 1/3840)))
(fma.f64 (pow.f64 x 3) -1/48 (fma.f64 (pow.f64 x 5) 1/3840 (*.f64 x 1/2)))
(fma.f64 (pow.f64 x 3) -1/48 (fma.f64 x 1/2 (*.f64 (pow.f64 x 5) 1/3840)))
(fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) -1/48 (*.f64 (pow.f64 x 5) 1/3840)))
(+.f64 (.f64 -1/645120 (pow.f64 x 7)) (+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 1/2 x) (.f64 1/3840 (pow.f64 x 5)))))
(fma.f64 -1/645120 (pow.f64 x 7) (fma.f64 -1/48 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (pow.f64 x 5) 1/3840))))
(fma.f64 (pow.f64 x 7) -1/645120 (fma.f64 (pow.f64 x 3) -1/48 (fma.f64 (pow.f64 x 5) 1/3840 (*.f64 x 1/2))))
(fma.f64 (pow.f64 x 3) -1/48 (fma.f64 (pow.f64 x 7) -1/645120 (fma.f64 x 1/2 (*.f64 (pow.f64 x 5) 1/3840))))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 x 1/2))

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 (*.f64 x 1/2))
✓	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)))
✓	14.6b	(/.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)

series8.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	-inf	(.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	inf	(.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))
0.0ms	x	@	0	(.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)))

rewrite84.0ms (0.8%)

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

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

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

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

simplify72.0ms (0.7%)

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))

eval207.0ms (2.1%)

Compiler: Compiled 7732 to 5797 computations (25% saved)

prune89.0ms (0.9%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	400	33	433
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	402	33	435

Error

0.0b

Counts

435 → 33

Alt Table

Click to see full alt table

Status	Error	Program
	15.5b	(/.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2)))) 3) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
	0.6b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
	31.3b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	43.9b	(.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))))
	44.7b	(/.f64 (.f64 x (.f64 x (fma.f64 x (*.f64 x -1/18) 2/3))) (sin.f64 x))
	31.3b	(/.f64 (log.f64 (pow.f64 (exp.f64 8/3) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))) (sin.f64 x))
	31.3b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
	30.1b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))))
	14.9b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
	31.3b	(.f64 8/3 (/.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 x))) (sin.f64 x)))
	44.5b	(/.f64 (.f64 2/3 (.f64 x x)) (sin.f64 x))
	0.6b	(.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (/.f64 1 (sin.f64 x))))
	14.8b	(/.f64 (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
	14.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
▶	31.3b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
	14.9b	(/.f64 (pow.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) 2) (sin.f64 x))
	31.3b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (+.f64 1/2 (.f64 -1/2 (cos.f64 x))) 8/3)))
	26.0b	(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 6) 1/3) (/.f64 8/3 (sin.f64 x)))
	1.3b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 x))))
	30.2b	(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
	30.7b	(/.f64 (.f64 (log.f64 (pow.f64 (exp.f64 8/3) (sin.f64 (.f64 x 1/2)))) (sin.f64 (*.f64 x 1/2))) (sin.f64 x))
	44.5b	(.f64 (.f64 x (*.f64 x 1/4)) (/.f64 8/3 (sin.f64 x)))
	30.2b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
	31.3b	(+.f64 0 (/.f64 8/3 (/.f64 (sin.f64 x) (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))))
	31.3b	(pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (-.f64 1/2 (.f64 1/2 (cos.f64 x))))) -1)
▶	30.0b	(*.f64 2/3 x)
▶	14.8b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
▶	0.5b	(.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
	31.3b	(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (-.f64 1/2 (*.f64 1/2 (cos.f64 x)))))
	31.3b	(/.f64 (*.f64 (/.f64 8/3 (sin.f64 x)) (-.f64 1 (cos.f64 x))) 2)
▶	30.2b	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
	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)))
	40.1b	(/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2)))) 2) (sin.f64 (.f64 x 1/2))) (sin.f64 x))

Compiler

Compiled 950 to 772 computations (18.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 42 to 30 computations (28.6% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite102.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 122

Calls

Call 1

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

Outputs

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

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

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

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

732×	`distribute-lft-out_binary64`
724×	`fma-def_binary64`
518×	`unswap-sqr_binary64`
506×	`associate-l_binary64`
402×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	486
1	152	484
2	362	482
3	1038	482
4	3344	482
5	5286	482
6	7900	482

Stop Event

1×	node limit

Counts

158 → 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 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)))
4/3
(+.f64 (*.f64 1/6 (pow.f64 x 2)) 4/3)
(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 4/3 (.f64 5/288 (pow.f64 x 4))))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 4/3 (+.f64 (.f64 5/288 (pow.f64 x 4)) (*.f64 61/34560 (pow.f64 x 6)))))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 8/3 (/.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))

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

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series3.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite43.0ms (0.4%)

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))))))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

Calls

Call 1

Inputs

Outputs

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 x)
✓	0.1b	(*.f64 (sin.f64 x) 3/8)
✓	0.2b	(/.f64 (-.f64 1 (cos.f64 x)) (.f64 (.f64 (sin.f64 x) 3/8) 2))
✓	1.7b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 34 to 21 computations (38.2% saved)

series7.0ms (0.1%)

Counts

4 → 32

Calls

12 calls:

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

rewrite144.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 209

Calls

Call 1

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

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

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

241 → 244

Calls

Call 1

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

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

localize38.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 (*.f64 x 1/2))
✓	0.2b	(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
✓	0.3b	(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
✓	14.6b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))

Compiler

Compiled 39 to 30 computations (23.1% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite100.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	231	38
2	2734	38

Stop Event

1×	node limit

Counts

3 → 110

Calls

Call 1

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

Outputs

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simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

146 → 139

Calls

Call 1

Inputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(*.f64 2/3 (pow.f64 x 2))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (.f64 2/3 (pow.f64 x 2)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (*.f64 1/540 (pow.f64 x 6))))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (+.f64 (.f64 -1/30240 (pow.f64 x 8)) (.f64 1/540 (pow.f64 x 6)))))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)

Outputs
(*.f64 2/3 x)
(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
(fma.f64 1/18 (pow.f64 x 3) (*.f64 2/3 x))
(fma.f64 2/3 x (*.f64 1/18 (pow.f64 x 3)))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 2/3 x) (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x)))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 3))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 2/3 x))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(fma.f64 2/3 x (fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (*.f64 17/30240 (pow.f64 x 7)))))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))
(*.f64 2/3 (pow.f64 x 2))
(.f64 2/3 (.f64 x x))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (.f64 2/3 (pow.f64 x 2)))
(fma.f64 -1/18 (pow.f64 x 4) (.f64 2/3 (.f64 x x)))
(fma.f64 2/3 (.f64 x x) (.f64 -1/18 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/18) 2/3))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/18) 2/3)))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (*.f64 1/540 (pow.f64 x 6))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (.f64 1/540 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/18) 2/3) (*.f64 1/540 (pow.f64 x 6)))
(fma.f64 2/3 (.f64 x x) (fma.f64 -1/18 (pow.f64 x 4) (.f64 1/540 (pow.f64 x 6))))
(+.f64 (.f64 -1/18 (pow.f64 x 4)) (+.f64 (.f64 2/3 (pow.f64 x 2)) (+.f64 (.f64 -1/30240 (pow.f64 x 8)) (.f64 1/540 (pow.f64 x 6)))))
(fma.f64 -1/18 (pow.f64 x 4) (fma.f64 2/3 (.f64 x x) (fma.f64 -1/30240 (pow.f64 x 8) (.f64 1/540 (pow.f64 x 6)))))
(fma.f64 2/3 (.f64 x x) (fma.f64 -1/18 (pow.f64 x 4) (fma.f64 1/540 (pow.f64 x 6) (.f64 -1/30240 (pow.f64 x 8)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/18) 2/3) (fma.f64 1/540 (pow.f64 x 6) (*.f64 -1/30240 (pow.f64 x 8))))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 1/2 x)) 2))
(.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))
(*.f64 1/4 (pow.f64 x 2))
(.f64 (.f64 x x) 1/4)
(.f64 x (.f64 x 1/4))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 -1/48 (pow.f64 x 4)))
(fma.f64 1/4 (.f64 x x) (.f64 (pow.f64 x 4) -1/48))
(fma.f64 (.f64 x x) 1/4 (.f64 (pow.f64 x 4) -1/48))
(fma.f64 x (.f64 x 1/4) (.f64 (pow.f64 x 4) -1/48))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/48) 1/4))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -1/48 1/4))
(+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (*.f64 -1/48 (pow.f64 x 4))))
(fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 (pow.f64 x 4) -1/48)))
(fma.f64 (.f64 x x) 1/4 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440)))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/48) 1/4) (*.f64 (pow.f64 x 6) 1/1440))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 6) 1/1440 (.f64 (pow.f64 x 4) -1/48)))
(+.f64 (.f64 -1/80640 (pow.f64 x 8)) (+.f64 (.f64 1/4 (pow.f64 x 2)) (+.f64 (.f64 1/1440 (pow.f64 x 6)) (.f64 -1/48 (pow.f64 x 4)))))
(fma.f64 -1/80640 (pow.f64 x 8) (fma.f64 1/4 (.f64 x x) (fma.f64 1/1440 (pow.f64 x 6) (.f64 (pow.f64 x 4) -1/48))))
(fma.f64 (pow.f64 x 8) -1/80640 (fma.f64 (.f64 x x) 1/4 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440))))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 8) -1/80640 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 6) 1/1440))))
(fma.f64 x (.f64 x 1/4) (fma.f64 (pow.f64 x 6) 1/1440 (fma.f64 (pow.f64 x 4) -1/48 (.f64 (pow.f64 x 8) -1/80640))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 1/2 x)) 2)
(pow.f64 (sin.f64 (*.f64 x 1/2)) 2)

localize46.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 50 to 35 computations (30% saved)

series21.0ms (0.2%)

Counts

4 → 28

Calls

12 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
4.0ms	x	@	0	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
4.0ms	x	@	inf	(pow.f64 (/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x))) 2)
1.0ms	x	@	0	(/.f64 (.f64 (sqrt.f64 8/3) (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 x)))
1.0ms	x	@	0	(sqrt.f64 (sin.f64 x))

rewrite135.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 155

Calls

Call 1

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

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

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

183 → 168

Calls

Call 1

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

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

eval457.0ms (4.6%)

Compiler: Compiled 16783 to 11889 computations (29.2% saved)

prune156.0ms (1.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	840	12	852
Fresh	25	3	28
Picked	1	0	1
Done	2	2	4
Total	868	17	885

Error

Counts

885 → 17

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.3b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	31.3b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
	31.5b	(exp.f64 (log.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
	14.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
✓	30.0b	(*.f64 2/3 x)
	30.6b	(log.f64 (exp.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
✓	14.8b	(/.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)) (sin.f64 x))
▶	0.4b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
	44.8b	(fabs.f64 (*.f64 2/3 x))
▶	0.2b	(pow.f64 (/.f64 1 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)) -1)
	31.3b	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
	31.3b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
	1.0b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (/.f64 x 2)) 3/4)))
▶	0.2b	(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))
	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))
▶	60.0b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
	31.3b	(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4)))

Compiler

Compiled 346 to 295 computations (14.7% saved)

localize14.0ms (0.1%)

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)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite59.0ms (0.6%)

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)))))))

simplify171.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

35 → 32

Calls

Call 1

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

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

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 2/3 x))
	0.3b	(*.f64 2/3 x)
✓	2.9b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series2.0ms (0%)

Counts

2 → 18

Calls

6 calls:

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

rewrite234.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	9
2	2109	9

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

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

Outputs

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

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

97 → 81

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify165.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

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))))

localize22.0ms (0.2%)

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)

series5.0ms (0%)

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))

rewrite66.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 64

Calls

Call 1

Inputs
(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)))))))))

simplify153.0ms (1.5%)

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))))

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x))))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 2 (-.f64 1 (cos.f64 x)))) (/.f64 8/3 (sin.f64 x)))
	0.4b	(/.f64 8/3 (sin.f64 x))
	1.7b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 44 to 29 computations (34.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 100

Calls

Call 1

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

Outputs

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

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

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

124 → 118

Calls

Call 1

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

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

eval191.0ms (1.9%)

Compiler: Compiled 6765 to 5296 computations (21.7% saved)

prune126.0ms (1.3%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	476	9	485
Fresh	4	6	10
Picked	1	0	1
Done	3	3	6
Total	484	18	502

Error

Counts

502 → 18

Alt Table

Click to see full alt table

Status	Error	Program
	31.3b	(/.f64 (.f64 (-.f64 1 (cos.f64 x)) 8/3) (.f64 2 (sin.f64 x)))
	0.3b	(/.f64 1 (/.f64 3/4 (tan.f64 (*.f64 x 1/2))))
	31.3b	(/.f64 (/.f64 8/3 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x))))
	14.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (pow.f64 (*.f64 (sin.f64 x) 3/8) -1))
	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 3/4 (cos.f64 (*.f64 x 1/2))))
▶	30.7b	(-.f64 (+.f64 1 (.f64 4/3 (tan.f64 (.f64 x 1/2)))) 1)
	60.0b	(-.f64 (-.f64 (+.f64 (*.f64 2/3 x) 2) 1) 1)
✓	60.0b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
▶	61.2b	(-.f64 1 1)
✓	0.4b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
▶	44.8b	(fabs.f64 (*.f64 2/3 x))
	29.9b	(pow.f64 (/.f64 3/2 x) -1)
▶	0.2b	(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)
▶	31.3b	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
	31.3b	(*.f64 4/3 (/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x)))
	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))
✓	30.0b	(*.f64 2/3 x)
	31.3b	(neg.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) -3/4)))

Compiler

Compiled 339 to 288 computations (15% saved)

localize11.0ms (0.1%)

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)

rewrite51.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify165.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

35 → 32

Calls

Call 1

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

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

localize2.0ms (0%)

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

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 10 to 7 computations (30% saved)

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 1 (.f64 4/3 (tan.f64 (.f64 x 1/2))))
✓	0.4b	(.f64 4/3 (tan.f64 (.f64 x 1/2)))
✓	3.0b	(-.f64 (+.f64 1 (.f64 4/3 (tan.f64 (.f64 x 1/2)))) 1)

Compiler

Compiled 36 to 30 computations (16.7% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite87.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

573×	`unpow-prod-down_binary64`
401×	`log-prod_binary64`
396×	`prod-diff_binary64`
389×	`fma-def_binary64`
244×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	219	28
2	2805	28

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

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

Outputs

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

simplify187.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

675×	`sqr-pow_binary64`
639×	`cube-prod_binary64`
624×	`unswap-sqr_binary64`
621×	`fma-def_binary64`
519×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	571
1	90	569
2	192	569
3	485	569
4	799	569
5	1577	569
6	2273	569
7	3222	569
8	3375	569
9	3621	569
10	3936	569
11	4417	569
12	5096	569
13	5990	569
14	6636	569
15	7145	569
16	7544	569
17	7923	569

Stop Event

1×	node limit

Counts

264 → 183

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

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sin.f64 x))
✓	0.1b	(/.f64 (-.f64 1 (cos.f64 x)) 3/4)
✓	0.2b	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
	1.7b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 33 to 20 computations (39.4% saved)

series5.0ms (0%)

Counts

3 → 28

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
0.0ms	x	@	inf	(/.f64 (-.f64 1 (cos.f64 x)) 3/4)
0.0ms	x	@	-inf	(/.f64 (-.f64 1 (cos.f64 x)) 3/4)
0.0ms	x	@	0	(*.f64 (/.f64 1 (sin.f64 x)) (/.f64 (-.f64 1 (cos.f64 x)) 3/4))
0.0ms	x	@	0	(/.f64 1 (sin.f64 x))

rewrite86.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

498×	`log-prod_binary64`
384×	`exp-prod_binary64`
315×	`pow-prod-down_binary64`
275×	`pow2_binary64`
193×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	223	29
2	2966	24

Stop Event

1×	node limit

Counts

3 → 148

Calls

Call 1

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

Outputs

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

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

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

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
742×	`distribute-lft-out_binary64`
725×	`distribute-rgt-out_binary64`
652×	`associate-l_binary64`
528×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	321
1	157	321
2	371	321
3	1092	305
4	4202	305
5	6643	305
6	7307	305

Stop Event

1×	node limit

Counts

176 → 173

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 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 4/3 (-.f64 1 (cos.f64 x)))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(/.f64 1 x)
(+.f64 (*.f64 1/6 x) (/.f64 1 x))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 7/360 (pow.f64 x 3)) (/.f64 1 x)))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 31/15120 (pow.f64 x 5)) (+.f64 (*.f64 7/360 (pow.f64 x 3)) (/.f64 1 x))))

Outputs
(*.f64 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))))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (*.f64 1/18 (pow.f64 x 3))))
(+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 17/30240 (pow.f64 x 7)) (+.f64 (.f64 2/3 x) (.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 2/3 x (*.f64 1/180 (pow.f64 x 5)))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 17/30240 (pow.f64 x 7) (fma.f64 1/180 (pow.f64 x 5) (*.f64 2/3 x))))
(fma.f64 1/18 (pow.f64 x 3) (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 2/3 x))))
(fma.f64 2/3 x (fma.f64 1/180 (pow.f64 x 5) (fma.f64 17/30240 (pow.f64 x 7) (*.f64 1/18 (pow.f64 x 3)))))
(fma.f64 x (fma.f64 x (.f64 x 1/18) 2/3) (fma.f64 1/180 (pow.f64 x 5) (.f64 17/30240 (pow.f64 x 7))))
(*.f64 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 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)))
(fma.f64 x (.f64 2/3 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 2/3 (.f64 x x) (fma.f64 -1/18 (pow.f64 x 4) (.f64 1/540 (pow.f64 x 6))))
(fma.f64 2/3 (.f64 x x) (fma.f64 1/540 (pow.f64 x 6) (.f64 -1/18 (pow.f64 x 4))))
(+.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)))))
(fma.f64 2/3 (.f64 x x) (fma.f64 1/540 (pow.f64 x 6) (fma.f64 -1/18 (pow.f64 x 4) (.f64 -1/30240 (pow.f64 x 8)))))
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(*.f64 4/3 (-.f64 1 (cos.f64 x)))
(+.f64 4/3 (*.f64 -4/3 (cos.f64 x)))
(fma.f64 -4/3 (cos.f64 x) 4/3)
(/.f64 1 x)
(+.f64 (*.f64 1/6 x) (/.f64 1 x))
(fma.f64 1/6 x (/.f64 1 x))
(fma.f64 x 1/6 (/.f64 1 x))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 7/360 (pow.f64 x 3)) (/.f64 1 x)))
(fma.f64 1/6 x (fma.f64 7/360 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/6 (fma.f64 (pow.f64 x 3) 7/360 (/.f64 1 x)))
(+.f64 (.f64 1/6 x) (+.f64 (.f64 31/15120 (pow.f64 x 5)) (+.f64 (*.f64 7/360 (pow.f64 x 3)) (/.f64 1 x))))
(fma.f64 1/6 x (fma.f64 31/15120 (pow.f64 x 5) (fma.f64 7/360 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 x 1/6 (fma.f64 (pow.f64 x 5) 31/15120 (fma.f64 (pow.f64 x 3) 7/360 (/.f64 1 x))))
(fma.f64 x 1/6 (fma.f64 (pow.f64 x 3) 7/360 (fma.f64 (pow.f64 x 5) 31/15120 (/.f64 1 x))))
(fma.f64 x (fma.f64 x (*.f64 x 7/360) 1/6) (fma.f64 31/15120 (pow.f64 x 5) (/.f64 1 x)))

eval193.0ms (1.9%)

Compiler: Compiled 7030 to 5567 computations (20.8% saved)

prune79.0ms (0.8%)

Pruning

16 alts after pruning (9 fresh and 7 done)

	Pruned	Kept	Total
New	463	5	468
Fresh	6	4	10
Picked	1	0	1
Done	0	7	7
Total	470	16	486

Error

Counts

486 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (cbrt.f64 4/3) 3) (tan.f64 (.f64 x 1/2)))
	31.4b	(/.f64 (-.f64 4/3 (*.f64 (cos.f64 x) 4/3)) (sin.f64 x))
	31.3b	(/.f64 (-.f64 1 (cos.f64 x)) (/.f64 (sin.f64 x) 4/3))
✓	30.7b	(-.f64 (+.f64 1 (.f64 4/3 (tan.f64 (.f64 x 1/2)))) 1)
	60.0b	(-.f64 (-.f64 (+.f64 (*.f64 2/3 x) 2) 1) 1)
✓	60.0b	(-.f64 (+.f64 1 (*.f64 2/3 x)) 1)
✓	61.2b	(-.f64 1 1)
✓	0.4b	(*.f64 4/3 (tan.f64 (/.f64 x 2)))
✓	44.8b	(fabs.f64 (*.f64 2/3 x))
	29.9b	(pow.f64 (/.f64 3/2 x) -1)
✓	0.2b	(/.f64 (tan.f64 (*.f64 x 1/2)) 3/4)
	19.9b	(cbrt.f64 (.f64 64/27 (pow.f64 (tan.f64 (.f64 x 1/2)) 3)))
	31.3b	(/.f64 (/.f64 8/3 (sin.f64 x)) (/.f64 2 (-.f64 1 (cos.f64 x))))
	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))
✓	30.0b	(*.f64 2/3 x)
	0.3b	(/.f64 1 (/.f64 3/4 (tan.f64 (/.f64 x 2))))

Compiler

Compiled 145 to 125 computations (13.8% saved)

regimes158.0ms (1.6%)

Counts

61 → 1

Calls

Call 1

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

Outputs
(+.f64 0 (/.f64 (tan.f64 (/.f64 x 2)) 3/4))

Calls

3 calls:

71.0ms	(/.f64 (.f64 (.f64 (/.f64 8 3) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (sin.f64 x))
34.0ms	x
31.0ms	(/.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))`
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 735 to 544 computations (26% saved)

regimes9.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
0.2b	1	`x`

Compiler

Compiled 67 to 56 computations (16.4% saved)

regimes8.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
29.9b	1	`x`

Compiler

Compiled 55 to 46 computations (16.4% saved)

regimes89.0ms (0.9%)

Accuracy

Total -32.2b remaining (-107.5%)

Threshold costs -32.2b (-107.5%)

Counts

6 → 1

Calls

Call 1

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

Outputs
(*.f64 2/3 x)

Calls

1 calls:

87.0ms

Results

Error	Segments	Branch
30.0b	1	`x`

Compiler

Compiled 50 to 42 computations (16% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`+-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	22	29

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 24 to 20 computations (16.7% saved)

soundness11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 83 to 68 computations (18.1% saved)

end31.0ms (0.3%)

Compiler: Compiled 21 to 17 computations (19% saved)