Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze139.0ms (2.5%)

Memory

-1.4MiB live, 140.1MiB allocated; 51ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample2.2s (38.8%)

Memory

21.7MiB live, 1 429.8MiB allocated; 419ms collecting garbage

Samples

813.0ms	2 250×	2	valid
544.0ms	4 104×	0	valid
349.0ms	734×	3	valid
207.0ms	1 165×	1	valid
3.0ms	3×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-cos: 1.1s (63.4% of total)

ival-sin: 260.0ms (15.7% of total)

adjust: 155.0ms (9.3% of total)

ival-sub!: 96.0ms (5.8% of total)

ival-div!: 96.0ms (5.8% of total)

Bogosity

preprocess56.0ms (1%)

Memory

9.4MiB live, 9.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	44	12
2	140	12
3	740	12

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Symmetry

(negabs x)

Compiler

Compiled 12 to 12 computations (0% saved)

series4.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated; 0ms collecting garbage

Counts

6 → 21

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))

Calls

3 calls:

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

rewrite964.0ms (17.2%)

Memory

-18.9MiB live, 270.5MiB allocated; 50ms collecting garbage

Counts

27 → 79

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))

Outputs
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 (neg.f64 x)))
(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (*.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (sin.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)))) (neg.f64 (sin.f64 (neg.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (fma.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x))))))
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 (neg.f64 x))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(tan.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))))
#s(literal 1 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 (fabs.f64 #s(literal 1 binary64)) (fabs.f64 #s(literal 1 binary64)))
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))) (pow.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))))
(+.f64 #s(literal 1 binary64) #s(literal 0 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) #s(literal 2 binary64))
(/.f64 (neg.f64 #s(literal 2 binary64)) (neg.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 #s(literal 0 binary64)))) #s(literal 2 binary64))
(cosh.f64 #s(literal 0 binary64))
(cosh.f64 (neg.f64 #s(literal 0 binary64)))
(exp.f64 #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 1 binary64)) #s(literal 3 binary64)))
(exp.f64 (*.f64 #s(literal 0 binary64) #s(literal 3 binary64)))
(exp.f64 (*.f64 #s(literal 0 binary64) #s(literal 2 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(fma.f64 (fabs.f64 #s(literal 1 binary64)) (fabs.f64 #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (pow.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))) (pow.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))) #s(literal 0 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 2 binary64))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 x)
(cos.f64 (neg.f64 x))
(cos.f64 (neg.f64 (neg.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
x
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(sin.f64 x)
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/720 binary64)) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx x x)
#s(approx (sin x) x)
#s(approx (sin x) (fma.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)) x x))
#s(approx (sin x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 (.f64 x x) x) x))
#s(approx (sin x) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (tan (/ x 2)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))

eval8.0ms (0.1%)

Memory: 13.8MiB live, 13.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 526 to 309 computations (41.3% saved)

prune6.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	8	74

Accuracy

100.0%

Counts

74 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(approx (sin x) x))
▶	4.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
▶	99.7%	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
▶	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
	51.7%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
▶	51.6%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
	51.5%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	51.6%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 142 to 134 computations (5.6% saved)

series8.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Counts

22 → 61

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(*.f64 x x)
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(sin.f64 x)
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(cos.f64 (/.f64 x #s(literal 2 binary64)))

Outputs
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx (cos (/ x 2)) #s(hole binary64 1))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (sin (/ x 2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (/ x 2)) #s(hole binary64 (cos (* 1/2 x))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((tan (/ x 2)) (/ x 2) x 2 (tan (/ x 2)) (* 1/2 x) 1/2 (tan (/ x 2)) (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) (+ (* (* x x) 1/240) 1/24) (* x x) 1/240 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))
2.0ms	x	@	-inf	((tan (/ x 2)) (/ x 2) x 2 (tan (/ x 2)) (* 1/2 x) 1/2 (tan (/ x 2)) (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) (+ (* (* x x) 1/240) 1/24) (* x x) 1/240 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))
2.0ms	x	@	0	((tan (/ x 2)) (/ x 2) x 2 (tan (/ x 2)) (* 1/2 x) 1/2 (tan (/ x 2)) (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) (+ (* (* x x) 1/240) 1/24) (* x x) 1/240 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))

Time

Variable

Point

Expression

2.0ms

inf

((tan (/ x 2)) (/ x 2) x 2 (tan (/ x 2)) (* 1/2 x) 1/2 (tan (/ x 2)) (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) (+ (* (* x x) 1/240) 1/24) (* x x) 1/240 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))

2.0ms

-inf

((tan (/ x 2)) (/ x 2) x 2 (tan (/ x 2)) (* 1/2 x) 1/2 (tan (/ x 2)) (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) (+ (* (* x x) 1/240) 1/24) (* x x) 1/240 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))

2.0ms

((tan (/ x 2)) (/ x 2) x 2 (tan (/ x 2)) (* 1/2 x) 1/2 (tan (/ x 2)) (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) (+ (* (* x x) 1/240) 1/24) (* x x) 1/240 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))

rewrite664.0ms (11.8%)

Memory

-5.8MiB live, 511.7MiB allocated; 150ms collecting garbage

Counts

83 → 140

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(*.f64 x x)
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(sin.f64 x)
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(cos.f64 (/.f64 x #s(literal 2 binary64)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx (cos (/ x 2)) #s(hole binary64 1))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (sin (/ x 2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (/ x 2)) #s(hole binary64 (cos (* 1/2 x))))
#s(approx (* (+ (* (+ (* (* x x) 1/240) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

Outputs
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(tan.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)))
(/.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 x) (neg.f64 #s(literal 2 binary64)))
x
#s(literal 2 binary64)
(+.f64 #s(literal 1 binary64) #s(literal 1 binary64))
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
(neg.f64 #s(literal -1/2 binary64))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))))
(+.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))))) (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 #s(literal 1/240 binary64)) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64)) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x))) (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64))) (-.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (+.f64 (pow.f64 #s(literal 1/24 binary64) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64) (-.f64 (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x))) (.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 #s(literal 1/24 binary64) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64)) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x x)
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
(*.f64 #s(literal 1/24 binary64) #s(literal 1 binary64))
(neg.f64 #s(literal -1/24 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(cosh.f64 #s(literal 0 binary64))
(exp.f64 #s(literal 0 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(approx (cos x) #s(literal 1 binary64))
(sin.f64 x)
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(tan.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(cos.f64 (/.f64 x #s(literal 2 binary64)))
(cos.f64 (neg.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
#s(approx x x)
#s(approx (* 1/2 x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) x) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (* (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) x) (.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) #s(literal 1/2 binary64))
#s(approx (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(literal 1/24 binary64))
#s(approx (+ 1/24 (* 1/240 (* x x))) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 x x) #s(literal 1/3840 binary64)) (.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (cos (/ x 2)) #s(literal 1 binary64))
#s(approx (cos (/ x 2)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (/ x 2)) (fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (/ x 2)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 x x) #s(literal 1/384 binary64)) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (tan (/ x 2)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64)))
#s(approx (* (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) x) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) x) (.f64 (+.f64 (+.f64 #s(literal 1/240 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64)))
#s(approx (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) (.f64 (+.f64 (+.f64 #s(literal 1/240 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1/24 (* 1/240 (* x x))) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
#s(approx (+ 1/24 (* 1/240 (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x)))
#s(approx (tan (/ x 2)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))
#s(approx (tan (/ x 2)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (sin (/ x 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (cos (/ x 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (+ 1/2 (* (+ 1/24 (* 1/240 (* x x))) (* x x))) x) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))))

eval12.0ms (0.2%)

Memory: 21.6MiB live, 21.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 962 to 493 computations (48.8% saved)

prune11.0ms (0.2%)

Memory

-34.8MiB live, 12.4MiB allocated; 7ms collecting garbage

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	3	3
Picked	3	2	5
Done	0	0	0
Total	108	9	117

Accuracy

100.0%

Counts

117 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(approx (sin x) x))
▶	4.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
	99.7%	(/.f64 (sin.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))) (cos.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))))
▶	100.0%	(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
▶	51.6%	#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
▶	51.7%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.6%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	51.5%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.6%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 168 to 155 computations (7.7% saved)

series11.0ms (0.2%)

Memory

15.0MiB live, 15.0MiB allocated; 0ms collecting garbage

Counts

27 → 84

Calls

Call 1

Inputs
(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (sin x) x)
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x))
(.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)

Outputs
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 1/240))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 (+ 1/240 (* 17/40320 (pow x 2)))))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 17/40320 (pow x 7))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* 17/40320 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (* 17/40320 (pow x 4))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 (* 17/40320 (pow x 2))))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((tan (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) (* (* x x) (+ (* (* x x) 1/240) 1/24)) (+ (* (* x x) 1/240) 1/24) 1/240 (tan (/ x 2)) (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (+ (* (* x x) 17/40320) 1/240) 17/40320)
3.0ms	x	@	0	((tan (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) (* (* x x) (+ (* (* x x) 1/240) 1/24)) (+ (* (* x x) 1/240) 1/24) 1/240 (tan (/ x 2)) (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (+ (* (* x x) 17/40320) 1/240) 17/40320)
3.0ms	x	@	-inf	((tan (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) (* (* x x) (+ (* (* x x) 1/240) 1/24)) (+ (* (* x x) 1/240) 1/24) 1/240 (tan (/ x 2)) (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (+ (* (* x x) 17/40320) 1/240) 17/40320)

Time

Variable

Point

Expression

3.0ms

inf

((tan (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) (* (* x x) (+ (* (* x x) 1/240) 1/24)) (+ (* (* x x) 1/240) 1/24) 1/240 (tan (/ x 2)) (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (+ (* (* x x) 17/40320) 1/240) 17/40320)

3.0ms

((tan (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) (* (* x x) (+ (* (* x x) 1/240) 1/24)) (+ (* (* x x) 1/240) 1/24) 1/240 (tan (/ x 2)) (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (+ (* (* x x) 17/40320) 1/240) 17/40320)

3.0ms

-inf

((tan (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) (* (* x x) (+ (* (* x x) 1/240) 1/24)) (+ (* (* x x) 1/240) 1/24) 1/240 (tan (/ x 2)) (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (+ (* (* x x) 17/40320) 1/240) 17/40320)

rewrite643.0ms (11.5%)

Memory

29.4MiB live, 261.4MiB allocated; 45ms collecting garbage

Counts

111 → 212

Calls

Call 1

Inputs
(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (sin x) x)
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x))
(.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 1/240))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 (+ 1/240 (* 17/40320 (pow x 2)))))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (* (* x x) (+ (* (* x x) 1/240) 1/24)) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 17/40320 (pow x 7))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* 17/40320 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (* 17/40320 (pow x 4))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 (* 17/40320 (pow x 2))))
#s(approx (+ (* (* x x) 17/40320) 1/240) #s(hole binary64 (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ (* (* x x) 1/240) 1/24)) x)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))))
#s(approx (* (+ (* (+ (* (+ (* (* x x) 17/40320) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))))

Outputs
(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
(neg.f64 #s(literal -1/2 binary64))
x
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(cosh.f64 #s(literal 0 binary64))
(exp.f64 #s(literal 0 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (sin x) x)
#s(approx (tan (/ x 2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/24 binary64) (*.f64 x x)) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
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(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (+.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 #s(literal 1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
#s(literal 1/24 binary64)
(*.f64 #s(literal 1/24 binary64) #s(literal 1 binary64))
(neg.f64 #s(literal -1/24 binary64))
#s(approx (tan (/ x 2)) (.f64 x (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(+.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x))))
(-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x))) x))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)))))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) x (.f64 #s(literal 1/2 binary64) x))
(fma.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) (.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))))
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) x)
(.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)))
(.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) x))
(.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))
(.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (.f64 x x))))
(+.f64 (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 x x)) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (.f64 x x))) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (*.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (*.f64 x x)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (*.f64 x x))))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (*.f64 x x))))
(fma.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 x x) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 #s(literal 1/240 binary64)) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64)) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x))) (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64))) (-.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (+.f64 (pow.f64 #s(literal 1/24 binary64) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64) (-.f64 (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x))) (.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 #s(literal 1/24 binary64) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (.f64 #s(literal 1/240 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64)) (.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 #s(literal 1/240 binary64) #s(literal 1 binary64))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 x (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
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(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x))))
(+.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)))
(+.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 x x)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x))))
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(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
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(+.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x)))
(+.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x)) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x)))) (-.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x))))
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(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x #s(literal 1/24 binary64))
(+.f64 #s(literal 1/240 binary64) (.f64 #s(literal 17/40320 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 17/40320 binary64) (.f64 x x)) #s(literal 1/240 binary64))
(-.f64 #s(literal 1/240 binary64) (.f64 (neg.f64 #s(literal 17/40320 binary64)) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal 1/240 binary64) #s(literal 1/240 binary64)) (.f64 (.f64 #s(literal 17/40320 binary64) (.f64 x x)) (.f64 #s(literal 17/40320 binary64) (.f64 x x)))) (-.f64 #s(literal 1/240 binary64) (.f64 #s(literal 17/40320 binary64) (.f64 x x))))
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(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 17/40320 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 #s(literal 1/240 binary64) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 17/40320 binary64) (.f64 x x)) (.f64 #s(literal 17/40320 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/240 binary64) #s(literal 1/240 binary64)) (.f64 (.f64 #s(literal 17/40320 binary64) (.f64 x x)) #s(literal 1/240 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 x (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* 1/2 x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx x x)
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 x (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
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#s(approx (cos x) #s(literal 1 binary64))
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#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
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#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(literal 1/2 binary64))
#s(approx (+ 1/2 (* 1/24 (* x x))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* 1/240 (* x x)))))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* 1/240 (* x x)))))) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* 1/240 (* x x)))))) (.f64 x (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) x)))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (.f64 (.f64 (.f64 x x) x) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(literal 1/24 binary64))
#s(approx (+ 1/24 (* 1/240 (* x x))) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (.f64 x (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) #s(literal 1/2 binary64))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) #s(literal 1/24 binary64))
#s(approx (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))
#s(approx (+ 1/240 (* 17/40320 (* x x))) #s(literal 1/240 binary64))
#s(approx (+ 1/240 (* 17/40320 (* x x))) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))
#s(approx (tan (/ x 2)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (tan (/ x 2)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) x)))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) x)))
#s(approx (+ 1/2 (* 1/24 (* x x))) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
#s(approx (+ 1/2 (* 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x)))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* 1/240 (* x x)))))) (*.f64 #s(literal 1/240 binary64) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* 1/240 (* x x)))))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* 1/240 (* x x)))))) (.f64 (+.f64 (+.f64 #s(literal 1/240 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (*.f64 #s(literal 1/240 binary64) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (*.f64 #s(literal 1/240 binary64) (pow.f64 x #s(literal 4 binary64))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1/24 (* 1/240 (* x x))) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
#s(approx (+ 1/24 (* 1/240 (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x)))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64)))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/240 binary64) (.f64 x x))) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (.f64 (+.f64 (+.f64 #s(literal 17/40320 binary64) (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 #s(literal 1/2 binary64) (pow.f64 x (neg.f64 #s(literal 6 binary64))) (/.f64 #s(literal 1/240 binary64) (.f64 x x)))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64)))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 6 binary64))))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) (.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/240 binary64) (.f64 x x))) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 6 binary64))))
#s(approx (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) (.f64 (+.f64 (+.f64 #s(literal 17/40320 binary64) (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 #s(literal 1/2 binary64) (pow.f64 x (neg.f64 #s(literal 6 binary64))) (/.f64 #s(literal 1/240 binary64) (.f64 x x)))) (pow.f64 x #s(literal 6 binary64))))
#s(approx (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64)))
#s(approx (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/240 binary64) (.f64 x x))) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1/240 (* 17/40320 (* x x))) (.f64 #s(literal 17/40320 binary64) (.f64 x x)))
#s(approx (+ 1/240 (* 17/40320 (* x x))) (.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 17/40320 binary64)) (*.f64 x x)))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* 1/240 (* x x)))))) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x))) #s(literal 17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ 1/2 (* (+ 1/24 (* (+ 1/240 (* 17/40320 (* x x))) (* x x))) (* x x))) x) (neg.f64 (.f64 (-.f64 (-.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 17/40320 binary64)) (/.f64 #s(literal 1/240 binary64) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64)))))

eval31.0ms (0.5%)

Memory: -19.4MiB live, 25.9MiB allocated; 5ms collecting garbage
Compiler: Compiled 2 231 to 959 computations (57% saved)

prune12.0ms (0.2%)

Memory

13.9MiB live, 13.9MiB allocated; 0ms collecting garbage

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	202	5	207
Fresh	0	2	2
Picked	1	4	5
Done	0	2	2
Total	203	13	216

Accuracy

100.0%

Counts

216 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(approx (sin x) x))
✓	4.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
▶	99.7%	(/.f64 (sin.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))) (cos.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))))
▶	27.9%	(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
▶	28.4%	(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
✓	100.0%	(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
✓	51.6%	#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
▶	51.5%	#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)))
✓	51.6%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
	51.7%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
✓	51.5%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	26.5%	#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x))
✓	51.6%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 251 to 237 computations (5.6% saved)

series15.0ms (0.3%)

Memory

-39.4MiB live, 10.9MiB allocated; 7ms collecting garbage

Counts

29 → 84

Calls

Call 1

Inputs
(/.f64 (sin.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))) (cos.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))))
(sin.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(cos.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(*.f64 x x)
#s(approx (sin x) x)
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x))
(.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)
(.f64 (.f64 x x) #s(approx (+ 1/24 (* 1/240 (* x x))) #s(literal 1/24 binary64)))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x))
(.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x)
#s(approx (+ 1/2 (* 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x)))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))
(+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))

Outputs
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (cos (/ x 2)) #s(hole binary64 1))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (* 1/2 (* x x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 1/24))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* -1/24 (pow x 2)))))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 1/2))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 1/2))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) (pow x 2))))
#s(approx (/ 1/2 (* x x)) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (sin (/ x 2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (/ x 2)) #s(hole binary64 (cos (* 1/2 x))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* -1/24 (pow x 4))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 (* -1/24 (pow x 2))))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 1/24))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 (+ 1/24 (* 1/2 (/ 1 (pow x 2))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (cos (/ x 2)) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* 1/2 (* x x)) (* x x) (sin x) (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (+ 1/24 (* 1/240 (* x x))) 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* (+ (* -1/24 (* x x)) 1/2) (* x x)) (+ (* -1/24 (* x x)) 1/2) -1/24 (tan (/ x 2)) (* (+ 1/2 (* 1/24 (* x x))) x) (+ 1/2 (* 1/24 (* x x))) (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) (+ 1/24 (/ 1/2 (* x x))) (/ 1/2 (* x x)))
3.0ms	x	@	-inf	((/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (cos (/ x 2)) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* 1/2 (* x x)) (* x x) (sin x) (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (+ 1/24 (* 1/240 (* x x))) 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* (+ (* -1/24 (* x x)) 1/2) (* x x)) (+ (* -1/24 (* x x)) 1/2) -1/24 (tan (/ x 2)) (* (+ 1/2 (* 1/24 (* x x))) x) (+ 1/2 (* 1/24 (* x x))) (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) (+ 1/24 (/ 1/2 (* x x))) (/ 1/2 (* x x)))
2.0ms	x	@	0	((/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (cos (/ x 2)) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* 1/2 (* x x)) (* x x) (sin x) (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (+ 1/24 (* 1/240 (* x x))) 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* (+ (* -1/24 (* x x)) 1/2) (* x x)) (+ (* -1/24 (* x x)) 1/2) -1/24 (tan (/ x 2)) (* (+ 1/2 (* 1/24 (* x x))) x) (+ 1/2 (* 1/24 (* x x))) (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) (+ 1/24 (/ 1/2 (* x x))) (/ 1/2 (* x x)))

Time

Variable

Point

Expression

3.0ms

inf

((/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (cos (/ x 2)) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* 1/2 (* x x)) (* x x) (sin x) (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (+ 1/24 (* 1/240 (* x x))) 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* (+ (* -1/24 (* x x)) 1/2) (* x x)) (+ (* -1/24 (* x x)) 1/2) -1/24 (tan (/ x 2)) (* (+ 1/2 (* 1/24 (* x x))) x) (+ 1/2 (* 1/24 (* x x))) (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) (+ 1/24 (/ 1/2 (* x x))) (/ 1/2 (* x x)))

3.0ms

-inf

((/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (cos (/ x 2)) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* 1/2 (* x x)) (* x x) (sin x) (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (+ 1/24 (* 1/240 (* x x))) 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* (+ (* -1/24 (* x x)) 1/2) (* x x)) (+ (* -1/24 (* x x)) 1/2) -1/24 (tan (/ x 2)) (* (+ 1/2 (* 1/24 (* x x))) x) (+ 1/2 (* 1/24 (* x x))) (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) (+ 1/24 (/ 1/2 (* x x))) (/ 1/2 (* x x)))

2.0ms

((/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (/ x 2) (* 1/2 x) 1/2 x (cos (/ x 2)) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* 1/2 (* x x)) (* x x) (sin x) (tan (/ x 2)) (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) (* (* x x) (+ 1/24 (* 1/240 (* x x)))) (+ 1/24 (* 1/240 (* x x))) 1/24 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) (* (+ (* -1/24 (* x x)) 1/2) (* x x)) (+ (* -1/24 (* x x)) 1/2) -1/24 (tan (/ x 2)) (* (+ 1/2 (* 1/24 (* x x))) x) (+ 1/2 (* 1/24 (* x x))) (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) (+ 1/24 (/ 1/2 (* x x))) (/ 1/2 (* x x)))

rewrite697.0ms (12.4%)

Memory

21.5MiB live, 327.3MiB allocated; 195ms collecting garbage

Counts

113 → 164

Calls

Call 1

Inputs
(/.f64 (sin.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))) (cos.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))))
(sin.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(cos.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(*.f64 x x)
#s(approx (sin x) x)
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x))
(.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)
(.f64 (.f64 x x) #s(approx (+ 1/24 (* 1/240 (* x x))) #s(literal 1/24 binary64)))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x))
(.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x)
#s(approx (+ 1/2 (* 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x)))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))
(+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (cos (/ x 2)) #s(hole binary64 1))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (* 1/2 (* x x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 1/24))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* -1/24 (pow x 2)))))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* 1/2 x)))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 1/2))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 1/2))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) (pow x 2))))
#s(approx (/ 1/2 (* x x)) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (sin (/ x 2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (/ x 2)) #s(hole binary64 (cos (* 1/2 x))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (* (* x x) (+ 1/24 (* 1/240 (* x x)))) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ 1/24 (* 1/240 (* x x))) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* -1/24 (pow x 4))))
#s(approx (* (+ (* -1/24 (* x x)) 1/2) (* x x)) #s(hole binary64 (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 (* -1/24 (pow x 2))))
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (+ 1/24 (/ 1/2 (* x x))) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 1/24))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(hole binary64 (+ 1/24 (* 1/2 (/ 1 (pow x 2))))))
#s(approx (+ (* x 1/2) (* (* (* x x) (+ 1/24 (* 1/240 (* x x)))) x)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))

Outputs
(/.f64 (sin.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))) (cos.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))))
(sin.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64))
x
(cos.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
#s(approx (sin x) x)
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( (* x x) 1/240)) #s(literal 1/24 binary64))) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( (* x x) 1/240)) #s(literal 1/24 binary64))) x))
(.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( (* x x) 1/240)) #s(literal 1/24 binary64))) x)
(.f64 (.f64 x x) #s(approx (+ 1/24 (* (* x x) 1/240)) #s(literal 1/24 binary64)))
#s(approx (+ 1/24 (* (* x x) 1/240)) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 #s(literal 1/24 binary64) #s(literal 1 binary64))
(neg.f64 #s(literal -1/24 binary64))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (.f64 x x))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (*.f64 x x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (*.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (.f64 #s(literal -1/24 binary64) (.f64 x x)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) (.f64 #s(literal -1/24 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal -1/24 binary64) x) x #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
(neg.f64 #s(literal 1/24 binary64))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x))
(.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x)
#s(approx (+ 1/2 (* 1/24 (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))
(.f64 (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 x x)))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(fma.f64 (.f64 #s(literal 1/24 binary64) x) x (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x x)))
(fma.f64 (.f64 #s(literal 1/24 binary64) x) x (.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x x)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64))
(-.f64 #s(literal 1/24 binary64) (.f64 (neg.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(/.f64 (+.f64 (pow.f64 #s(literal 1/24 binary64) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/24 binary64) #s(literal 1/24 binary64) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/24 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/24 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) x)
(/.f64 (neg.f64 #s(literal 1/2 binary64)) (neg.f64 (*.f64 x x)))
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 x x) #s(literal 1/3840 binary64)) (.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* 1/2 x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx x x)
#s(approx (cos (/ x 2)) #s(literal 1 binary64))
#s(approx (cos (/ x 2)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (/ x 2)) (fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (/ x 2)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 x x) #s(literal 1/384 binary64)) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (* 1/2 (* x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240))))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240))))) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240))))) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (* (* (* x x) (+ 1/24 (* (* x x) 1/240))) x) (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x))))
#s(approx (* (* (* x x) (+ 1/24 (* (* x x) 1/240))) x) (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))))
#s(approx (* (* x x) (+ 1/24 (* (* x x) 1/240))) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
#s(approx (* (* x x) (+ 1/24 (* (* x x) 1/240))) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)))
#s(approx (+ 1/24 (* (* x x) 1/240)) #s(literal 1/24 binary64))
#s(approx (+ 1/24 (* (* x x) 1/240)) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (* (+ 1/2 (* -1/24 (* x x))) (* x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (* (+ 1/2 (* -1/24 (* x x))) (* x x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ 1/2 (* -1/24 (* x x))) #s(literal 1/2 binary64))
#s(approx (+ 1/2 (* -1/24 (* x x))) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (+ 1/2 (* 1/24 (* x x))) #s(literal 1/2 binary64))
#s(approx (+ 1/2 (* 1/24 (* x x))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (* (* x x) (+ 1/24 (/ 1/2 (* x x)))) #s(literal 1/2 binary64))
#s(approx (* (* x x) (+ 1/24 (/ 1/2 (* x x)))) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (+ 1/24 (/ 1/2 (* x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
#s(approx (+ 1/24 (/ 1/2 (* x x))) (/.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (/ 1/2 (* x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
#s(approx (tan (/ x 2)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (sin (/ x 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (cos (/ x 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (tan (/ x 2)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (sin x) (sin.f64 x))
#s(approx (tan (/ x 2)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240))))) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64)))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240))))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240))))) (.f64 (+.f64 (+.f64 #s(literal 1/240 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (* (* x x) (+ 1/24 (* (* x x) 1/240))) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64)))
#s(approx (* (* (* x x) (+ 1/24 (* (* x x) 1/240))) x) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (* x x) (+ 1/24 (* (* x x) 1/240))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64)))
#s(approx (* (* x x) (+ 1/24 (* (* x x) 1/240))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1/24 (* (* x x) 1/240)) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
#s(approx (+ 1/24 (* (* x x) 1/240)) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x)))
#s(approx (* (+ 1/2 (* -1/24 (* x x))) (* x x)) (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64))))
#s(approx (* (+ 1/2 (* -1/24 (* x x))) (* x x)) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ 1/2 (* -1/24 (* x x))) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
#s(approx (+ 1/2 (* -1/24 (* x x))) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (*.f64 x x)))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x))))
#s(approx (* (+ 1/2 (* 1/24 (* x x))) x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))))
#s(approx (+ 1/2 (* 1/24 (* x x))) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
#s(approx (+ 1/2 (* 1/24 (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
#s(approx (* (* x x) (+ 1/24 (/ 1/2 (* x x)))) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
#s(approx (* (* x x) (+ 1/24 (/ 1/2 (* x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
#s(approx (+ 1/24 (/ 1/2 (* x x))) #s(literal 1/24 binary64))
#s(approx (+ 1/24 (/ 1/2 (* x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
#s(approx (* x (+ 1/2 (* (* x x) (+ 1/24 (* (* x x) 1/240))))) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))))

eval53.0ms (0.9%)

Memory: -24.2MiB live, 20.5MiB allocated; 8ms collecting garbage
Compiler: Compiled 1 525 to 756 computations (50.4% saved)

prune18.0ms (0.3%)

Memory

12.5MiB live, 12.5MiB allocated; 0ms collecting garbage

Pruning

20 alts after pruning (10 fresh and 10 done)

	Pruned	Kept	Total
New	151	8	159
Fresh	0	2	2
Picked	1	4	5
Done	0	6	6
Total	152	20	172

Accuracy

100.0%

Counts

172 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(approx (sin x) x))
✓	4.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
✓	99.7%	(/.f64 (sin.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))) (cos.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))))
	27.9%	(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) x) x #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
	27.7%	(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	27.9%	(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
	3.7%	(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(approx (+ 1/2 ( -1/24 (* x x))) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (*.f64 x x))) #s(approx (sin x) x))
	27.9%	(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
✓	28.4%	(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
	26.1%	(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))) #s(approx (sin x) x))
✓	100.0%	(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
✓	51.6%	#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
✓	51.5%	#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)))
✓	51.6%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
	51.7%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
✓	51.5%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
	26.4%	#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (.f64 x x))) x))
✓	26.5%	#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x))
	26.0%	#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 #s(approx (+ 1/24 (/ 1/2 ( x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x))) x))
✓	51.6%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 473 to 401 computations (15.2% saved)

regimes17.0ms (0.3%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 #s(approx (+ 1/24 (/ 1/2 ( x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x))) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(approx (+ 1/2 ( -1/24 (* x x))) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (*.f64 x x))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) x) x #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (.f64 x x))) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(approx (sin x) x))
(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))) (cos.f64 #s(approx (/ x 2) (.f64 #s(literal 1/2 binary64) x))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))

Outputs
(tan.f64 #s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x)))

Calls

2 calls:

8.0ms	x
7.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
100.0%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes14.0ms (0.3%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 #s(approx (+ 1/24 (/ 1/2 ( x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x))) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(approx (+ 1/2 ( -1/24 (* x x))) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (*.f64 x x))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) x) x #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (.f64 x x))) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(approx (sin x) x))

Outputs
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))

Outputs

#s(approx (tan (/ x 2)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))

Calls

2 calls:

7.0ms	x
6.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
51.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
51.7%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes17.0ms (0.3%)

Memory

-46.3MiB live, 7.5MiB allocated; 11ms collecting garbage

Accuracy

Total -32.4b remaining (-104.5%)

Threshold costs -32.4b (-104.5%)

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) #s(approx (+ 1/24 ( 1/240 (* x x))) #s(literal 1/24 binary64))) x)))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 #s(approx (+ 1/24 (/ 1/2 ( x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x))) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(approx (+ 1/2 ( -1/24 (* x x))) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (*.f64 x x))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) x) x #s(literal 1/2 binary64)) (*.f64 x x))) #s(approx (sin x) x))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))) x))
#s(approx (tan (/ x 2)) (.f64 #s(approx (+ 1/2 ( 1/24 (* x x))) (.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (.f64 x x))) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(approx (sin x) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (tan (/ x 2)) (fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))) x)))
(/.f64 #s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))) #s(approx (sin x) x))

Outputs
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Calls

2 calls:

12.0ms	x
4.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
51.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
51.6%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

derivations1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 24 to 19 computations (20.8% saved)

preprocess36.0ms (0.6%)

Memory: 40.5MiB live, 40.5MiB allocated; 0ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 94 to 87 computations (7.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze139.0ms (2.5%)

sample2.2s (38.8%)

preprocess56.0ms (1%)

series4.0ms (0.1%)

rewrite964.0ms (17.2%)

eval8.0ms (0.1%)

prune6.0ms (0.1%)

series8.0ms (0.1%)

rewrite664.0ms (11.8%)

eval12.0ms (0.2%)

prune11.0ms (0.2%)

series11.0ms (0.2%)

rewrite643.0ms (11.5%)

eval31.0ms (0.5%)

prune12.0ms (0.2%)

series15.0ms (0.3%)

rewrite697.0ms (12.4%)

eval53.0ms (0.9%)

prune18.0ms (0.3%)

regimes17.0ms (0.3%)

regimes14.0ms (0.3%)

regimes17.0ms (0.3%)

derivations1.0ms (0%)

preprocess36.0ms (0.6%)

end0.0ms (0%)

Profiling