Metrics for ENA, Section 1.4, Mentioned, A

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.6%	50.4%	0%	0%	0%	0
100%	49.6%	0%	50.4%	0%	0%	0%	1

Compiler

Compiled 12 to 9 computations (25% saved)

sample2.6s (64.1%)

Results

1.9s	4375×	body	2048	valid
426.0ms	2102×	body	1024	valid
139.0ms	999×	body	512	valid
64.0ms	780×	body	256	valid

Bogosity

preprocess208.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

52×	`fma-def`
18×	`sub-neg`
14×	`associate--r+`
12×	`associate-+l-`
12×	`neg-mul-1`

Problems

135×	`(-.f64 1 (cos.f64 x))`
121×	No Errors

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	60
1	22	56
2	41	56
3	63	56
4	103	56
5	128	56
6	138	56
7	140	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 (neg.f64 x)))
(neg.f64 (-.f64 1 (cos.f64 (neg.f64 x))))

Outputs
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 (neg.f64 x)))
(-.f64 1 (cos.f64 x))
(neg.f64 (-.f64 1 (cos.f64 (neg.f64 x))))
(neg.f64 (-.f64 1 (cos.f64 x)))
(+.f64 -1 (cos.f64 x))
(+.f64 (cos.f64 x) -1)

Symmetry

(abs x)

Compiler

Compiled 15 to 10 computations (33.3% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.4%	(-.f64 1 (cos.f64 x))
▶	52.4%	(-.f64 1 (cos.f64 x))

Compiler

Compiled 10 to 8 computations (20% saved)

localize73.0ms (1.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	52.4%	(-.f64 1 (cos.f64 x))

Compiler

Compiled 10 to 6 computations (40% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite120.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`unpow-prod-down`
363×	`log1p-expm1-u`
363×	`expm1-log1p-u`
341×	`add-exp-log`
328×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	79	14
2	948	14

Stop Event

1×	node limit

Counts

1 → 61

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))

Outputs
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 0 (-.f64 1 (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(+.f64 (log.f64 (E.f64)) (neg.f64 (cos.f64 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4)))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)) (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4)) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 5)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(/.f64 1 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2) (neg.f64 (cos.f64 x)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (-.f64 1 (neg.f64 (cos.f64 x))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (-.f64 1 (pow.f64 (cos.f64 x) 3)))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))) -1)
(pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (.f64 (.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(fma.f64 1 (neg.f64 (cos.f64 x)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)
(fma.f64 (cbrt.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 -1 (cos.f64 x) 1)
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)
(fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1806×	`times-frac`
1002×	`associate-/l*`
828×	`fma-def`
754×	`associate-/r*`
588×	`div-sub`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	2086
1	388	1957
2	1027	1877
3	3594	1873

Stop Event

1×	node limit

Counts

65 → 86

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/40320 (pow.f64 x 8)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 0 (-.f64 1 (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(+.f64 (log.f64 (E.f64)) (neg.f64 (cos.f64 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (-.f64 1 (cos.f64 x)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4)))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)) (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4)) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 5)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(/.f64 1 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2) (neg.f64 (cos.f64 x)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (-.f64 1 (neg.f64 (cos.f64 x))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (-.f64 1 (pow.f64 (cos.f64 x) 3)))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))) -1)
(pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (.f64 (.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(fma.f64 1 (neg.f64 (cos.f64 x)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)
(fma.f64 (cbrt.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 -1 (cos.f64 x) 1)
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)
(fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)

Outputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 2) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (pow.f64 x 2) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/40320 (pow.f64 x 8)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/720 (pow.f64 x 6)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 1/2 (pow.f64 x 2) (*.f64 -1/40320 (pow.f64 x 8)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 0 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(+.f64 (log.f64 (E.f64)) (neg.f64 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))
(-.f64 1 (cos.f64 x))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (cos.f64 x)) (log.f64 (E.f64)))
(-.f64 1 (cos.f64 x))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(-.f64 1 (cos.f64 x))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4)))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)))
(*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/4) (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/4) (pow.f64 (-.f64 1 (cos.f64 x)) 1/4))
(*.f64 (pow.f64 1 1/3) (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 (cos.f64 x)) (cbrt.f64 (-.f64 1 (cos.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 5/2)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)) (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/2)))
(*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/4) (sqrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3/4) (pow.f64 (-.f64 1 (cos.f64 x)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 4)) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 5)) (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 5)))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (cos.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 5/2))
(/.f64 1 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2) (neg.f64 (cos.f64 x)))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (-.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (-.f64 1 (neg.f64 (cos.f64 x))))
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (-.f64 1 (pow.f64 (cos.f64 x) 3)))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (pow.f64 (-.f64 1 (cos.f64 x)) 2))) (cbrt.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) (pow.f64 (sin.f64 x) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (-.f64 1 (cos.f64 x)) 2))) (cbrt.f64 (+.f64 1 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(-.f64 1 (cos.f64 x))
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)
(-.f64 1 (cos.f64 x))
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(-.f64 1 (cos.f64 x))
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(-.f64 1 (cos.f64 x))
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1) (-.f64 1 (pow.f64 (cos.f64 x) 3))) -1)
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)
(*.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 2)) (cbrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) (sqrt.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(-.f64 1 (cos.f64 x))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(-.f64 1 (cos.f64 x))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (.f64 (.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3))
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))
(pow.f64 (E.f64) (log1p.f64 (neg.f64 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(fma.f64 1 (neg.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (neg.f64 (cbrt.f64 (cos.f64 x))) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (sqrt.f64 (cos.f64 x)) (neg.f64 (sqrt.f64 (cos.f64 x))) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (cbrt.f64 (pow.f64 (neg.f64 (cos.f64 x)) 2)) (cbrt.f64 (neg.f64 (cos.f64 x))) 1)
(fma.f64 (sqrt.f64 (neg.f64 (cos.f64 x))) (sqrt.f64 (neg.f64 (cos.f64 x))) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 -1 (cos.f64 x) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(fma.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))

eval24.0ms (0.6%)

Compiler: Compiled 1033 to 692 computations (33% saved)

prune11.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Accuracy

100.0%

Counts

87 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.4%	(-.f64 1 (cos.f64 x))
▶	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	99.5%	(*.f64 1/2 (pow.f64 x 2))
✓	52.4%	(-.f64 1 (cos.f64 x))
▶	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	99.5%	(*.f64 1/2 (pow.f64 x 2))

Compiler

Compiled 38 to 30 computations (21.1% saved)

localize47.0ms (1.2%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	100.0%	(*.f64 1/2 (pow.f64 x 2))

Compiler

Compiled 31 to 21 computations (32.3% saved)

series4.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

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

rewrite61.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

978×	`unpow-prod-down`
742×	`log-prod`
638×	`log1p-expm1-u`
638×	`expm1-log1p-u`
474×	`pow-prod-down`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	43
1	157	43
2	1813	43

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

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

Outputs
(+.f64 (.f64 (pow.f64 x 2) 1/4) (.f64 (pow.f64 x 2) 1/4))
(+.f64 0 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2)))) 1)
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 1/8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (pow.f64 x 2)))))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (pow.f64 x 2))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) 1/8)) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 1/2))) 2))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))
(+.f64 0 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))) 1)
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 1)
(pow.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 3)
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 2) 1/2)
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 2)
(sqrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 3))
(expm1.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))
(exp.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 2))
(log1p.f64 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1686×	`log-prod`
944×	`fma-neg`
812×	`associate-r`
748×	`fma-def`
716×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	135	1664
1	289	1589
2	798	1589
3	4067	1589
4	7136	1589

Stop Event

1×	node limit

Counts

56 → 65

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/40320 (pow.f64 x 8)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(+.f64 (.f64 (pow.f64 x 2) 1/4) (.f64 (pow.f64 x 2) 1/4))
(+.f64 0 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2)))) 1)
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 1/8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (pow.f64 x 2)))))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (pow.f64 x 2))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) 1/8)) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 1/2))) 2))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))
(+.f64 0 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))) 1)
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 1)
(pow.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 3)
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 2) 1/2)
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 2)
(sqrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 3))
(expm1.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))
(exp.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 2))
(log1p.f64 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 2) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (pow.f64 x 2) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/40320 (pow.f64 x 8)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/720 (pow.f64 x 6)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(+.f64 (.f64 (pow.f64 x 2) 1/4) (.f64 (pow.f64 x 2) 1/4))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 0 (*.f64 1/2 (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2)))))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(*.f64 3 (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))))
(*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))) 3)
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2)))) 1)
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1)
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))) 3)
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(pow.f64 (*.f64 (pow.f64 x 6) 1/8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(*.f64 1/2 (pow.f64 x 2))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (pow.f64 x 2)))))
(*.f64 1/2 (pow.f64 x 2))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (pow.f64 x 2))) 1))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))) 1) 1))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2)))) 3))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) 1/8)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 1/2))) 2))
(*.f64 1/2 (pow.f64 x 2))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 0 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (.f64 1/2 x))))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))) 1)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 1)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(pow.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 3)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 2) 1/2)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(pow.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 3) 1/3)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(pow.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 2)
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(sqrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 2))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))) 3))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(expm1.f64 (log1p.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))) 1) 1))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 3))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (.f64 (.f64 3 (log.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x))))) 1/3))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 2))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))
(log1p.f64 (expm1.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))))
(.f64 (sin.f64 x) (tan.f64 (.f64 1/2 x)))

eval25.0ms (0.6%)

Compiler: Compiled 736 to 567 computations (23% saved)

prune11.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	63	5	68

Accuracy

100.0%

Counts

68 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.9%	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
▶	100.0%	(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
✓	52.4%	(-.f64 1 (cos.f64 x))
✓	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	99.5%	(*.f64 1/2 (pow.f64 x 2))
▶	98.9%	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
▶	100.0%	(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
✓	52.4%	(-.f64 1 (cos.f64 x))
✓	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	99.5%	(*.f64 1/2 (pow.f64 x 2))

Compiler

Compiled 78 to 62 computations (20.5% saved)

localize156.0ms (3.9%)

Localize:

Found 5 expressions with local error:

New	Accuracy	Program
✓	99.6%	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
✓	99.3%	(*.f64 x (sqrt.f64 1/2))
✓	100.0%	(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
✓	100.0%	(.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))
✓	100.0%	(sin.f64 (*.f64 1/2 x))

Compiler

Compiled 51 to 36 computations (29.4% saved)

series6.0ms (0.1%)

Counts

5 → 40

Calls

15 calls:

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

rewrite90.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1095×	`log1p-expm1-u`
1084×	`prod-diff`
803×	`expm1-log1p-u`
386×	`expm1-udef`
386×	`log1p-udef`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	121
1	223	117
2	2983	117

Stop Event

1×	node limit

Counts

5 → 122

Calls

Call 1

Inputs
(sin.f64 (*.f64 1/2 x))
(.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)

Outputs
(-.f64 (exp.f64 (log1p.f64 (sin.f64 (*.f64 1/2 x)))) 1)
(.f64 (sin.f64 (.f64 1/2 x)) 1)
(.f64 1 (sin.f64 (.f64 1/2 x)))
(.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 1/2 x))) 2))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2) (cbrt.f64 (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (sin.f64 (.f64 1/2 x))) (sqrt.f64 (sin.f64 (*.f64 1/2 x))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (sin.f64 (*.f64 1/2 x))) 3)
(pow.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (sin.f64 (*.f64 1/2 x))) 2)
(sqrt.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (sin.f64 (*.f64 1/2 x))))
(log.f64 (+.f64 1 (expm1.f64 (sin.f64 (*.f64 1/2 x)))))
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (sin.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (sin.f64 (*.f64 1/2 x))))
(exp.f64 (.f64 (log.f64 (sin.f64 (.f64 1/2 x))) 1))
(log1p.f64 (expm1.f64 (sin.f64 (*.f64 1/2 x))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))) 1)
(-.f64 (/.f64 (cos.f64 (.f64 x -1/2)) 2) (/.f64 (cos.f64 (.f64 x 3/2)) 2))
(/.f64 (-.f64 (cos.f64 (.f64 x -1/2)) (cos.f64 (.f64 x 3/2))) 2)
(/.f64 1 (/.f64 2 (-.f64 (cos.f64 (.f64 x -1/2)) (cos.f64 (.f64 x 3/2)))))
(/.f64 (-.f64 (cos.f64 (-.f64 x (.f64 1/2 x))) (cos.f64 (.f64 x 3/2))) 2)
(/.f64 (neg.f64 (-.f64 (cos.f64 (.f64 x -1/2)) (cos.f64 (.f64 x 3/2)))) -2)
(pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 1)
(pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 3)
(pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2)
(sqrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 (*.f64 1/2 x))) (sin.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 3))
(cbrt.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (sin.f64 x) 3)))
(cbrt.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 (.f64 1/2 x)) 3)))
(expm1.f64 (log1p.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))))
(exp.f64 (log.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))) 1))
(log1p.f64 (expm1.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)))) 1)
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x))))
(.f64 (sin.f64 (.f64 1/2 x)) (.f64 (sin.f64 x) (/.f64 1 (cos.f64 (.f64 1/2 x)))))
(.f64 (sin.f64 x) (.f64 (sin.f64 (.f64 1/2 x)) (/.f64 1 (cos.f64 (.f64 1/2 x)))))
(.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (/.f64 1 (cos.f64 (.f64 1/2 x))))
(.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x)) 1)
(.f64 1 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) (.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (/.f64 1 (cos.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) (pow.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) 2) (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (/.f64 1 (cos.f64 (*.f64 1/2 x)))))
(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) (sqrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 1/2 x)) (neg.f64 (sin.f64 x))) (/.f64 1 (neg.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 1 (cos.f64 (.f64 1/2 x))) (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) 1) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (sin.f64 x) (cbrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (sin.f64 x) (sqrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 (sin.f64 x) (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (sin.f64 (.f64 1/2 x)) (sqrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 (sin.f64 x) 1) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cbrt.f64 (cos.f64 (*.f64 1/2 x)))))
(.f64 (/.f64 1 (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (sqrt.f64 (cos.f64 (*.f64 1/2 x)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) 1) (/.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (cos.f64 (.f64 1/2 x))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (sqrt.f64 (cos.f64 (*.f64 1/2 x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 1) (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (cos.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (cbrt.f64 (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 1)
(pow.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))) 2)
(pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))) -1)
(neg.f64 (/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (neg.f64 (cos.f64 (*.f64 1/2 x)))))
(sqrt.f64 (pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 2))
(log.f64 (exp.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)))))
(cbrt.f64 (pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(expm1.f64 (log1p.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(exp.f64 (log.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) 1))
(log1p.f64 (expm1.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2)))) 1)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 1)
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) 2)
(sqrt.f64 (*.f64 1/2 (pow.f64 x 2)))
(fabs.f64 (*.f64 x (sqrt.f64 1/2)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (sqrt.f64 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3))
(cbrt.f64 (.f64 (pow.f64 x 3) (.f64 1/2 (sqrt.f64 1/2))))
(cbrt.f64 (.f64 (.f64 1/2 (sqrt.f64 1/2)) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 1/2))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 1/2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2)))) 1)
(*.f64 1/2 (pow.f64 x 2))
(.f64 x (.f64 (sqrt.f64 1/2) (*.f64 x (sqrt.f64 1/2))))
(.f64 (sqrt.f64 1/2) (.f64 x (*.f64 x (sqrt.f64 1/2))))
(.f64 (.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(.f64 (.f64 1/2 (pow.f64 x 2)) 1)
(*.f64 (pow.f64 x 2) 1/2)
(.f64 1 (.f64 1/2 (pow.f64 x 2)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 1/2)) 4)) (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 1/2))) (.f64 (sqrt.f64 (.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(.f64 (.f64 (.f64 x (sqrt.f64 1/2)) (sqrt.f64 (.f64 x (sqrt.f64 1/2)))) (sqrt.f64 (*.f64 x (sqrt.f64 1/2))))
(.f64 (.f64 (*.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2))
(.f64 (.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)) x)
(.f64 (.f64 (.f64 x (sqrt.f64 1/2)) (cbrt.f64 (.f64 1/2 (pow.f64 x 2)))) (cbrt.f64 (*.f64 x (sqrt.f64 1/2))))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4))
(log.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (pow.f64 x 2)))))
(cbrt.f64 (pow.f64 (*.f64 1/2 (pow.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (pow.f64 x 2))) 1))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))

simplify101.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1470×	`fma-def`
1126×	`distribute-lft-in`
816×	`log-prod`
528×	`associate-r`
484×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	5207
1	715	5161
2	3145	5159

Stop Event

1×	node limit

Counts

162 → 170

Calls

Call 1

Inputs
(*.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 1/3840 (pow.f64 x 5)) (*.f64 1/2 x)))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 -1/645120 (pow.f64 x 7)) (+.f64 (.f64 1/3840 (pow.f64 x 5)) (.f64 1/2 x))))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -5/48 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(+.f64 (.f64 -5/48 (pow.f64 x 4)) (+.f64 (.f64 91/11520 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (.f64 -5/48 (pow.f64 x 4)) (+.f64 (.f64 -41/129024 (pow.f64 x 8)) (+.f64 (.f64 91/11520 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/40320 (pow.f64 x 8)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(-.f64 (exp.f64 (log1p.f64 (sin.f64 (*.f64 1/2 x)))) 1)
(.f64 (sin.f64 (.f64 1/2 x)) 1)
(.f64 1 (sin.f64 (.f64 1/2 x)))
(.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 1/2 x))) 2))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2) (cbrt.f64 (sin.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (sin.f64 (.f64 1/2 x))) (sqrt.f64 (sin.f64 (*.f64 1/2 x))))
(pow.f64 (sin.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (sin.f64 (*.f64 1/2 x))) 3)
(pow.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (sin.f64 (*.f64 1/2 x))) 2)
(sqrt.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (sin.f64 (*.f64 1/2 x))))
(log.f64 (+.f64 1 (expm1.f64 (sin.f64 (*.f64 1/2 x)))))
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (sin.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (sin.f64 (*.f64 1/2 x))))
(exp.f64 (.f64 (log.f64 (sin.f64 (.f64 1/2 x))) 1))
(log1p.f64 (expm1.f64 (sin.f64 (*.f64 1/2 x))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))) 1)
(-.f64 (/.f64 (cos.f64 (.f64 x -1/2)) 2) (/.f64 (cos.f64 (.f64 x 3/2)) 2))
(/.f64 (-.f64 (cos.f64 (.f64 x -1/2)) (cos.f64 (.f64 x 3/2))) 2)
(/.f64 1 (/.f64 2 (-.f64 (cos.f64 (.f64 x -1/2)) (cos.f64 (.f64 x 3/2)))))
(/.f64 (-.f64 (cos.f64 (-.f64 x (.f64 1/2 x))) (cos.f64 (.f64 x 3/2))) 2)
(/.f64 (neg.f64 (-.f64 (cos.f64 (.f64 x -1/2)) (cos.f64 (.f64 x 3/2)))) -2)
(pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 1)
(pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 3)
(pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2)
(sqrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 (*.f64 1/2 x))) (sin.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))))
(cbrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 3))
(cbrt.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (sin.f64 x) 3)))
(cbrt.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 (.f64 1/2 x)) 3)))
(expm1.f64 (log1p.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))))
(exp.f64 (log.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))) 1))
(log1p.f64 (expm1.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)))) 1)
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 x))))
(.f64 (sin.f64 (.f64 1/2 x)) (.f64 (sin.f64 x) (/.f64 1 (cos.f64 (.f64 1/2 x)))))
(.f64 (sin.f64 x) (.f64 (sin.f64 (.f64 1/2 x)) (/.f64 1 (cos.f64 (.f64 1/2 x)))))
(.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (/.f64 1 (cos.f64 (.f64 1/2 x))))
(.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x)) 1)
(.f64 1 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) (.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (/.f64 1 (cos.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) (pow.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) 2) (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (/.f64 1 (cos.f64 (*.f64 1/2 x)))))
(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) (sqrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(.f64 (.f64 (sin.f64 (.f64 1/2 x)) (neg.f64 (sin.f64 x))) (/.f64 1 (neg.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 1 (cos.f64 (.f64 1/2 x))) (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) 1) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (sin.f64 x) (cbrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (sin.f64 x) (sqrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 (sin.f64 x) (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (sin.f64 (.f64 1/2 x)) (sqrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 (sin.f64 x) 1) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))
(.f64 (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 (cos.f64 (.f64 1/2 x)))))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cbrt.f64 (cos.f64 (*.f64 1/2 x)))))
(.f64 (/.f64 1 (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (sqrt.f64 (cos.f64 (*.f64 1/2 x)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) 1) (/.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (cos.f64 (.f64 1/2 x))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 2) (sqrt.f64 (cos.f64 (.f64 1/2 x)))) (/.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (sqrt.f64 (cos.f64 (*.f64 1/2 x)))))
(.f64 (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) 1) (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (cos.f64 (.f64 1/2 x))))
(.f64 (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x))) (cbrt.f64 (cos.f64 (*.f64 1/2 x)))))
(pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 1)
(pow.f64 (cbrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))) 2)
(pow.f64 (/.f64 (cos.f64 (.f64 1/2 x)) (.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x))) -1)
(neg.f64 (/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (neg.f64 (cos.f64 (*.f64 1/2 x)))))
(sqrt.f64 (pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 2))
(log.f64 (exp.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)))))
(cbrt.f64 (pow.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) 3) (pow.f64 (cos.f64 (*.f64 1/2 x)) 3)))
(expm1.f64 (log1p.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(exp.f64 (log.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) (sin.f64 x))) 1))
(log1p.f64 (expm1.f64 (.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))) (sin.f64 x))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2)))) 1)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 1)
(pow.f64 (*.f64 1/2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) 2)
(sqrt.f64 (*.f64 1/2 (pow.f64 x 2)))
(fabs.f64 (*.f64 x (sqrt.f64 1/2)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (sqrt.f64 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3))
(cbrt.f64 (.f64 (pow.f64 x 3) (.f64 1/2 (sqrt.f64 1/2))))
(cbrt.f64 (.f64 (.f64 1/2 (sqrt.f64 1/2)) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 1/2))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 1/2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2)))) 1)
(*.f64 1/2 (pow.f64 x 2))
(.f64 x (.f64 (sqrt.f64 1/2) (*.f64 x (sqrt.f64 1/2))))
(.f64 (sqrt.f64 1/2) (.f64 x (*.f64 x (sqrt.f64 1/2))))
(.f64 (.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(.f64 (.f64 1/2 (pow.f64 x 2)) 1)
(*.f64 (pow.f64 x 2) 1/2)
(.f64 1 (.f64 1/2 (pow.f64 x 2)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 1/2)) 4)) (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 1/2))) (.f64 (sqrt.f64 (.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(.f64 (.f64 (.f64 x (sqrt.f64 1/2)) (sqrt.f64 (.f64 x (sqrt.f64 1/2)))) (sqrt.f64 (*.f64 x (sqrt.f64 1/2))))
(.f64 (.f64 (*.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2))
(.f64 (.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)) x)
(.f64 (.f64 (.f64 x (sqrt.f64 1/2)) (cbrt.f64 (.f64 1/2 (pow.f64 x 2)))) (cbrt.f64 (*.f64 x (sqrt.f64 1/2))))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4))
(log.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (pow.f64 x 2)))))
(cbrt.f64 (pow.f64 (*.f64 1/2 (pow.f64 x 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (pow.f64 x 2))) 1))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (.f64 1/2 x))
(fma.f64 -1/48 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 -1/48 (pow.f64 x 3)))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 1/3840 (pow.f64 x 5)) (*.f64 1/2 x)))
(fma.f64 -1/48 (pow.f64 x 3) (fma.f64 1/3840 (pow.f64 x 5) (*.f64 1/2 x)))
(fma.f64 -1/48 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 1/3840 (pow.f64 x 5))))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 -1/645120 (pow.f64 x 7)) (+.f64 (.f64 1/3840 (pow.f64 x 5)) (.f64 1/2 x))))
(fma.f64 -1/48 (pow.f64 x 3) (fma.f64 -1/645120 (pow.f64 x 7) (fma.f64 1/3840 (pow.f64 x 5) (*.f64 1/2 x))))
(fma.f64 -1/48 (pow.f64 x 3) (fma.f64 -1/645120 (pow.f64 x 7) (fma.f64 1/2 x (*.f64 1/3840 (pow.f64 x 5)))))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -5/48 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(fma.f64 -5/48 (pow.f64 x 4) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 2) (*.f64 -5/48 (pow.f64 x 4)))
(+.f64 (.f64 -5/48 (pow.f64 x 4)) (+.f64 (.f64 91/11520 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -5/48 (pow.f64 x 4) (fma.f64 91/11520 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -5/48 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (*.f64 91/11520 (pow.f64 x 6))))
(fma.f64 1/2 (pow.f64 x 2) (fma.f64 -5/48 (pow.f64 x 4) (*.f64 91/11520 (pow.f64 x 6))))
(+.f64 (.f64 -5/48 (pow.f64 x 4)) (+.f64 (.f64 -41/129024 (pow.f64 x 8)) (+.f64 (.f64 91/11520 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -5/48 (pow.f64 x 4) (fma.f64 -41/129024 (pow.f64 x 8) (fma.f64 91/11520 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -5/48 (pow.f64 x 4) (fma.f64 -41/129024 (pow.f64 x 8) (fma.f64 1/2 (pow.f64 x 2) (*.f64 91/11520 (pow.f64 x 6)))))
(fma.f64 -5/48 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (fma.f64 91/11520 (pow.f64 x 6) (*.f64 -41/129024 (pow.f64 x 8)))))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 2) (*.f64 (pow.f64 x 4) -1/24))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 (pow.f64 x 4) -1/24 (fma.f64 1/2 (pow.f64 x 2) (*.f64 (pow.f64 x 6) 1/720)))
(fma.f64 1/2 (pow.f64 x 2) (fma.f64 (pow.f64 x 4) -1/24 (*.f64 (pow.f64 x 6) 1/720)))
(+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/40320 (pow.f64 x 8)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 (pow.f64 x 4) -1/24 (fma.f64 (pow.f64 x 8) -1/40320 (fma.f64 1/2 (pow.f64 x 2) (*.f64 (pow.f64 x 6) 1/720))))
(fma.f64 (pow.f64 x 4) -1/24 (fma.f64 1/2 (pow.f64 x 2) (fma.f64 (pow.f64 x 6) 1/720 (*.f64 (pow.f64 x 8) -1/40320))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 1/2 (pow.f64 x 2))
(-.f64 (exp.f64 (log1p.f64 (sin.f64 (*.f64 1/2 x)))) 1)
(sin.f64 (*.f64 1/2 x))
(.f64 (sin.f64 (.f64 1/2 x)) 1)
(sin.f64 (*.f64 1/2 x))
(.f64 1 (sin.f64 (.f64 1/2 x)))
(sin.f64 (*.f64 1/2 x))
(.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 1/2 x))) 2))
(sin.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2) (cbrt.f64 (sin.f64 (*.f64 1/2 x))))
(sin.f64 (*.f64 1/2 x))
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(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (sqrt.f64 1/2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (sqrt.f64 1/2))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 1/2))) 1))
(*.f64 x (sqrt.f64 1/2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (sqrt.f64 1/2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2)))) 1)
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(.f64 x (.f64 (sqrt.f64 1/2) (*.f64 x (sqrt.f64 1/2))))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (sqrt.f64 1/2) (.f64 x (*.f64 x (sqrt.f64 1/2))))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 1/2 (pow.f64 x 2)) 1)
(*.f64 1/2 (pow.f64 x 2))
(*.f64 (pow.f64 x 2) 1/2)
(*.f64 1/2 (pow.f64 x 2))
(.f64 1 (.f64 1/2 (pow.f64 x 2)))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (.f64 (.f64 x (sqrt.f64 1/2)) (cbrt.f64 (*.f64 x (sqrt.f64 1/2)))))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) 4))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 1/2)) 4)) (cbrt.f64 (*.f64 1/2 (pow.f64 x 2))))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 1/2))) (.f64 (sqrt.f64 (.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 (.f64 x (sqrt.f64 1/2)) (sqrt.f64 (.f64 x (sqrt.f64 1/2)))) (sqrt.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 (*.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)) x)
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 (.f64 x (sqrt.f64 1/2)) (cbrt.f64 (.f64 1/2 (pow.f64 x 2)))) (cbrt.f64 (*.f64 x (sqrt.f64 1/2))))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (.f64 (.f64 x (sqrt.f64 1/2)) (cbrt.f64 (*.f64 x (sqrt.f64 1/2)))))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) 4))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4))
(*.f64 1/2 (pow.f64 x 2))
(log.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (pow.f64 x 2)))))
(*.f64 1/2 (pow.f64 x 2))
(cbrt.f64 (pow.f64 (*.f64 1/2 (pow.f64 x 2)) 3))
(*.f64 1/2 (pow.f64 x 2))
(expm1.f64 (log1p.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (log.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (pow.f64 x 2))) 1))
(*.f64 1/2 (pow.f64 x 2))
(log1p.f64 (expm1.f64 (*.f64 1/2 (pow.f64 x 2))))
(*.f64 1/2 (pow.f64 x 2))

eval79.0ms (2%)

Compiler: Compiled 2630 to 2017 computations (23.3% saved)

prune23.0ms (0.6%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	170	5	175

Accuracy

100.0%

Counts

175 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.9%	(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
✓	100.0%	(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))
✓	52.4%	(-.f64 1 (cos.f64 x))
✓	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	99.5%	(*.f64 1/2 (pow.f64 x 2))

Compiler

Compiled 74 to 57 computations (23% saved)

regimes12.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (cos.f64 (*.f64 1/2 x)))

Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Calls

3 calls:

5.0ms	(-.f64 1 (cos.f64 x))
4.0ms	x
2.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 1 (cos.f64 x))`
100.0%	1	`(cos.f64 x)`

Compiler

Compiled 45 to 33 computations (26.7% saved)

regimes8.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))
(*.f64 1/2 (pow.f64 x 2))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)

Outputs
(*.f64 1/2 (pow.f64 x 2))

Calls

3 calls:

3.0ms	x
2.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 1 (cos.f64 x))`
99.5%	1	`(cos.f64 x)`

Compiler

Compiled 26 to 20 computations (23.1% saved)

regimes8.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))

Outputs
(-.f64 1 (cos.f64 x))

Calls

3 calls:

4.0ms	x
2.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
52.4%	1	`x`
52.4%	1	`(-.f64 1 (cos.f64 x))`
52.4%	1	`(cos.f64 x)`

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
4×	`sub-neg`
4×	`+-commutative`
2×	`1-exp`
2×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	23	57
2	27	57
3	29	57
4	30	57

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

soundness211.0ms (5.2%)

Rules

1806×	`times-frac`
1002×	`associate-/l*`
828×	`fma-def`
754×	`associate-/r*`
588×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	79	14
2	948	14
0	179	2086
1	388	1957
2	1027	1877
3	3594	1873

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 131 to 76 computations (42% saved)

end0.0ms (0%)

preprocess43.0ms (1.1%)

Remove: (abs x)
Compiler: Compiled 130 to 96 computations (26.2% saved)

analyze0.0ms (0%)

sample2.6s (64.1%)

preprocess208.0ms (5.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize73.0ms (1.8%)

series1.0ms (0%)

rewrite120.0ms (3%)

simplify54.0ms (1.3%)

eval24.0ms (0.6%)

prune11.0ms (0.3%)

localize47.0ms (1.2%)

series4.0ms (0.1%)

rewrite61.0ms (1.5%)

simplify70.0ms (1.7%)

eval25.0ms (0.6%)

prune11.0ms (0.3%)

localize156.0ms (3.9%)

series6.0ms (0.1%)

rewrite90.0ms (2.2%)

simplify101.0ms (2.5%)

eval79.0ms (2%)

prune23.0ms (0.6%)

regimes12.0ms (0.3%)

regimes8.0ms (0.2%)

regimes8.0ms (0.2%)

simplify3.0ms (0.1%)

soundness211.0ms (5.2%)

end0.0ms (0%)

preprocess43.0ms (1.1%)

Profiling