Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

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

analyze32.0ms (0.3%)

Memory

-10.8MiB live, 33.8MiB allocated; 6ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.6s (71.1%)

Memory

222.9MiB live, 7 545.8MiB allocated; 2.7s collecting garbage

Samples

2.5s	5 805×	2	valid
2.4s	25 939×	0	invalid
622.0ms	2 410×	1	valid
6.0ms	41×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 4.0s

ival-cos: 2.5s (62.8% of total)

adjust: 386.0ms (9.7% of total)

ival-fabs: 304.0ms (7.6% of total)

ival-sub!: 188.0ms (4.7% of total)

ival-add!: 187.0ms (4.7% of total)

ival-<: 177.0ms (4.4% of total)

ival-mult!: 161.0ms (4% of total)

ival-and: 68.0ms (1.7% of total)

ival-assert: 13.0ms (0.3% of total)

Bogosity

explain199.0ms (2.1%)

Memory

11.5MiB live, 245.0MiB allocated; 23ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
125	2	(6.2566941084321925e-158 4.8923060666443574e-167)	1	(-957.8293381938112 0.049561253256488746)	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	0	-	0	-	`(cos.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	126	1
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	125	0
-	2	129

Precision

0.984251968503937

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	125	0	0
-	2	0	129

Precision?

0.984251968503937

Recall?

1.0

Freqs

test

number	freq
0	129
1	127

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

135.0ms	370×	2	valid
17.0ms	140×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-cos: 104.0ms (80.5% of total)

adjust: 19.0ms (14.7% of total)

ival-sub!: 3.0ms (2.3% of total)

ival-add!: 2.0ms (1.5% of total)

preprocess99.0ms (1.1%)

Memory

-10.2MiB live, 36.5MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	53	48
2	93	48
3	124	48
4	132	48
5	154	48
6	238	48
7	800	48
8	5175	48

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 14 to 12 computations (14.3% saved)

series5.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Counts

6 → 36

Calls

Call 1

Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#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 (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))

rewrite147.0ms (1.6%)

Memory

0.8MiB live, 184.4MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	544
0	153	528
1	883	525
0	8275	504

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

42 → 113

Calls

Call 1

Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#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 (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Outputs
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))))))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 eps))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (sin.f64 x))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x))))
(cos.f64 (neg.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(+.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))))
(+.f64 eps (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 eps x)
(+.f64 x (*.f64 (neg.f64 eps) #s(literal -1 binary64)))
(+.f64 x eps)
x
eps
(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 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 x))
(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)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 eps) x) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (cos (+ x eps)) (cos.f64 eps))
#s(approx (cos (+ x eps)) (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 eps) x) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx 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 #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 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (cos x) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (cos (+ x eps)) (cos.f64 x))
#s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx eps eps)
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 eps)))

eval17.0ms (0.2%)

Memory: 26.0MiB live, 26.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 982 to 429 computations (78.4% saved)

prune8.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	12	107

Accuracy

99.8%

Counts

107 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
	56.8%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
▶	56.7%	(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
	56.7%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
✓	56.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	55.8%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	83.4%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
▶	55.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
▶	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 363 to 270 computations (25.6% saved)

series41.0ms (0.4%)

Memory

-33.2MiB live, 56.9MiB allocated; 8ms collecting garbage

Counts

39 → 208

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(sin.f64 x)
x
#s(literal 1/6 binary64)
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(+.f64 eps x)
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (+.f64 eps x) x)
#s(literal -2 binary64)

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#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 #s(hole binary64 x))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 eps)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#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 (* -1/2 (cos x)) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (+ x (* 1/2 (PI)))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 x))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ eps (* 1/2 (PI))) (* -1 x)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin x)))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2)
7.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2)
5.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2)
5.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2)
5.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2)

rewrite201.0ms (2.2%)

Memory

36.2MiB live, 245.8MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	863	5780
0	918	5444
1	5208	5444
0	8040	5156

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

247 → 371

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(sin.f64 x)
x
#s(literal 1/6 binary64)
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(+.f64 eps x)
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (+.f64 eps x) x)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#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 #s(hole binary64 x))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 eps)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#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 (* -1/2 (cos x)) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (+ x (* 1/2 (PI)))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 x))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ eps (* 1/2 (PI))) (* -1 x)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin x)))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) (.f64 (sin.f64 x) (sin.f64 x))) (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))))
(-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(.f64 eps (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) eps))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) eps))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (-.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))) (-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))
(fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(-.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (neg.f64 eps) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))))
(-.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))
(+.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 x)) (.f64 #s(literal -1/6 binary64) (sin.f64 x)))) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))) (-.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64)) (.f64 #s(literal -1/216 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (fma.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 x)) (.f64 #s(literal -1/6 binary64) (sin.f64 x)) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/13824 binary64) (pow.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))))))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(fma.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
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(sin.f64 x)
x
#s(literal 1/6 binary64)
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 x))
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(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
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(cos.f64 eps)
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#s(literal 1 binary64)
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(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
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(fma.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps x))))
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
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(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x))))
(cos.f64 (neg.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
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(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) x)
(+.f64 (+.f64 eps x) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))
(/.f64 (neg.f64 (PI.f64)) #s(literal -2 binary64))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))
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(.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(literal -2 binary64)))
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(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
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(/.f64 (-.f64 (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (.f64 (cos.f64 x) (cos.f64 x))) (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
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(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
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(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(+.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps eps (fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) (.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (.f64 (+.f64 eps x) x))))
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(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (*.f64 #s(literal 2 binary64) x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+.f64 x (+.f64 eps x))
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(-.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (+.f64 eps x) x)) #s(literal -2 binary64))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
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(-.f64 (+.f64 eps x) x)
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#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (-.f64 (.f64 (+.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
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#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/36 binary64) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (.f64 eps x) #s(literal -1/36 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (*.f64 #s(literal 1/24 binary64) eps))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (.f64 eps x) #s(literal -1/48 binary64) #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps)))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #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 x x)
#s(approx (* (* (cos x) eps) 1/24) (*.f64 #s(literal 1/24 binary64) eps))
#s(approx (* (* (cos x) eps) 1/24) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/48 binary64) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* (* (cos x) eps) 1/24) (fma.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/48 binary64) eps)) (.f64 x x) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* (* (cos x) eps) 1/24) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/17280 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/576 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/48 binary64) eps)) (.f64 x x) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#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 #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 (* -1/2 (cos x)) #s(literal -1/2 binary64))
#s(approx (* -1/2 (cos x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (cos x)) (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (cos x)) (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1440 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(literal -2 binary64) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (fma.f64 (fma.f64 (.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) x (.f64 (.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (+ eps x) x) eps)
#s(approx (+ (+ eps x) x) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (/ (- (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (+ eps x) x) eps)
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (* (cos x) eps) 1/24) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)))
#s(approx (+ (/ (PI) 2) (+ eps x)) x)
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (+.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps) x) #s(literal 1 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) x)
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (+ eps x) x) (*.f64 #s(literal 2 binary64) x))
#s(approx (+ (+ eps x) x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps) (neg.f64 x))) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps) (neg.f64 x))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (neg.f64 x) (-.f64 (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps) x)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (+ eps x) x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (*.f64 (sin.f64 x) #s(literal 1/6 binary64)))
#s(approx eps eps)
#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))
#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/40320 binary64) (.f64 eps eps)) #s(literal 1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal -1/2 binary64))) eps (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal -1/2 binary64))) eps (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) eps) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) #s(literal -2 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/4 binary64) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/12 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (sin.f64 x))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (.f64 eps eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) eps))
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) eps)
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (+.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps) #s(literal 1 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (+ eps x) x) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) eps)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (neg.f64 eps))) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (neg.f64 eps))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))

eval53.0ms (0.6%)

Memory: 21.9MiB live, 88.8MiB allocated; 16ms collecting garbage
Compiler: Compiled 12 881 to 2 182 computations (83.1% saved)

prune27.0ms (0.3%)

Memory

2.1MiB live, 47.0MiB allocated; 7ms collecting garbage

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	380	22	402
Fresh	4	2	6
Picked	3	2	5
Done	1	0	1
Total	388	26	414

Accuracy

100.0%

Counts

414 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
	56.8%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
	99.6%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
▶	99.6%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
▶	99.5%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
▶	55.6%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
▶	99.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
✓	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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))))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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))))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	56.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
▶	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
	24.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64)))))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))

Compiler

Compiled 1 788 to 1 172 computations (34.5% saved)

series42.0ms (0.5%)

Memory

-31.0MiB live, 59.0MiB allocated; 14ms collecting garbage

Counts

42 → 220

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))))
(fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
(*.f64 eps x)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal 1/6 binary64)
(.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x))
(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps)
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(sin.f64 x)
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps)
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x)))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(literal -1/2 binary64)
(neg.f64 (sin.f64 x))

Outputs
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 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 (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#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 (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin x)))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* -1 (* eps x))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* -1/2 eps)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2))))))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 -1))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 (- (* 1/6 (pow eps 2)) 1)))
#s(approx (* (* eps eps) 1/6) #s(hole binary64 (* 1/6 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1 (sin x))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* 1/24 (pow eps 4))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (* 1/6 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 (* 1/6 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* 1/24 (pow eps 4))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x)) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* eps x) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (sin x) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (* (cos x) eps) (cos x) -1/2 (neg (sin x)))
8.0ms	eps	@	0	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* eps x) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (sin x) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (* (cos x) eps) (cos x) -1/2 (neg (sin x)))
7.0ms	x	@	0	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* eps x) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (sin x) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (* (cos x) eps) (cos x) -1/2 (neg (sin x)))
5.0ms	eps	@	inf	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* eps x) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (sin x) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (* (cos x) eps) (cos x) -1/2 (neg (sin x)))
4.0ms	x	@	inf	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* eps x) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (sin x) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (* (cos x) eps) (cos x) -1/2 (neg (sin x)))

rewrite207.0ms (2.2%)

Memory

48.9MiB live, 230.2MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	888	6722
0	934	6410
1	5377	6410
0	8312	6066

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

262 → 361

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))))
(fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
(*.f64 eps x)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal 1/6 binary64)
(.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x))
(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps)
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(sin.f64 x)
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps)
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x)))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(literal -1/2 binary64)
(neg.f64 (sin.f64 x))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 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 (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#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 (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin x)))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* -1 (* eps x))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* -1/2 eps)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/6 x))) 1/2))))))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 -1))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 (- (* 1/6 (pow eps 2)) 1)))
#s(approx (* (* eps eps) 1/6) #s(hole binary64 (* 1/6 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1 (sin x))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* 1/24 (pow eps 4))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (* 1/6 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 (* 1/6 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/6) 1) #s(hole binary64 (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* 1/24 (pow eps 4))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x)) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))

Outputs
(.f64 #s(literal -2 binary64) #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) x)))))
(sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) x)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) x)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) x)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x)) (.f64 eps eps)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x x)) (-.f64 (+.f64 x eps) x))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x))) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps eps (fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) (.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x) (-.f64 (.f64 eps eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 (+.f64 x eps) x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64))) (fma.f64 eps eps (-.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 2 binary64) x)) (.f64 eps (.f64 #s(literal 2 binary64) x)))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (*.f64 #s(literal 2 binary64) x) eps)
(+.f64 (+.f64 x eps) x)
(+.f64 x (+.f64 x eps))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
#s(literal 2 binary64)
x
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 x eps)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 x eps))))
(/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps))) (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))) (-.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) #s(literal 3 binary64))) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (-.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))))
(fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 x eps)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 x eps)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps) (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 x eps)))
(fma.f64 eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(-.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (.f64 (neg.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (.f64 eps eps)))
(-.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (.f64 (neg.f64 (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(+.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(+.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))
(*.f64 x eps)
(*.f64 eps x)
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 eps eps))
(.f64 eps (.f64 #s(literal 1/6 binary64) eps))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 eps #s(literal 2 binary64))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(literal 1/6 binary64)
(.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)
(.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))
(.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(.f64 eps (.f64 #s(literal 1/24 binary64) eps))
#s(literal 1/24 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps)) (.f64 (sin.f64 x) (sin.f64 x))) (fma.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)))))
(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x))
(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps)
(.f64 eps #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps)
(.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))))
(fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps))
(fma.f64 eps (neg.f64 (sin.f64 x)) (.f64 eps (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) eps) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps))
(+.f64 (.f64 eps (neg.f64 (sin.f64 x))) (.f64 eps (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x)))) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))) (-.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (-.f64 (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (neg.f64 (sin.f64 x))))))
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x)) (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))) (.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (neg.f64 (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
(fma.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps) (neg.f64 (sin.f64 x)))
(-.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)))
(+.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
(+.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (neg.f64 (sin.f64 x)))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
#s(literal -1/2 binary64)
(*.f64 #s(literal -1 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1 binary64))
(neg.f64 (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 (PI.f64)) (*.f64 (cos.f64 x) (sin.f64 (PI.f64))))
(sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (neg.f64 x))
(sin.f64 (+.f64 x (PI.f64)))
(-.f64 (.f64 (cos.f64 x) #s(literal 0 binary64)) (.f64 (sin.f64 x) #s(literal 1 binary64)))
(cos.f64 (neg.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 (PI.f64))) (.f64 (cos.f64 x) (sin.f64 (PI.f64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(literal -2 binary64) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) x (.f64 (.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* 2 x) eps) eps)
#s(approx (+ (* 2 x) eps) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx x x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (-.f64 (.f64 (+.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 x eps))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 x eps) (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 eps eps))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 x eps))))
#s(approx (* eps x) (*.f64 x eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/36 binary64) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (.f64 x eps) #s(literal 1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (.f64 x eps) #s(literal -1/36 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #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 (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) x (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#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 #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 (neg (sin x)) (neg.f64 x))
#s(approx (neg (sin x)) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))
#s(approx (neg (sin x)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64)) (.f64 x x)) #s(literal 1 binary64)) x))
#s(approx (neg (sin x)) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.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 (- (cos (+ x eps)) (cos x)) (.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) x)
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* 2 x) eps) (*.f64 #s(literal 2 binary64) x))
#s(approx (+ (* 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))) x))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (sin x) (sin.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) (cos.f64 x)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (neg (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* 2 x) eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x)))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (neg.f64 x) (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps) (neg.f64 x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) eps) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) #s(literal -2 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/4 binary64) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/12 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/4 binary64) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/12 binary64)) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/12 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 x))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (sin.f64 x)))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) eps (sin.f64 x)))
#s(approx eps eps)
#s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (* 1/2 eps) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/40320 binary64) (.f64 eps eps)) #s(literal 1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (neg.f64 eps) x))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))
#s(approx (- (* (* eps eps) 1/6) 1) #s(literal -1 binary64))
#s(approx (- (* (* eps eps) 1/6) 1) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
#s(approx (* (* eps eps) 1/6) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* (* eps eps) 1/24) 1/2) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (* (* eps eps) 1/24) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal -1/2 binary64))) eps (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) (cos.f64 x)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (neg.f64 (sin.f64 x)))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* 2 x) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) (/.f64 (neg.f64 x) (pow.f64 eps #s(literal 3 binary64)))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (* eps eps) 1/6) 1) (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))
#s(approx (- (* (* eps eps) 1/6) 1) (.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal -2 binary64))) (.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))
#s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (*.f64 eps eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (.f64 eps eps)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x)))
#s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 2 x) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps) #s(literal -1 binary64) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps))) eps) #s(literal -1 binary64) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) eps)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps))) (*.f64 eps eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (neg.f64 eps))) (cos.f64 x)))
#s(approx (+ (* (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps))))

eval51.0ms (0.5%)

Memory: -21.5MiB live, 81.1MiB allocated; 19ms collecting garbage
Compiler: Compiled 16 093 to 1 969 computations (87.8% saved)

prune28.0ms (0.3%)

Memory

4.7MiB live, 50.5MiB allocated; 5ms collecting garbage

Pruning

30 alts after pruning (26 fresh and 4 done)

	Pruned	Kept	Total
New	343	16	359
Fresh	9	10	19
Picked	3	2	5
Done	0	2	2
Total	355	30	385

Accuracy

100.0%

Counts

385 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
	56.8%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
▶	99.8%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
▶	99.5%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
	99.4%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	99.6%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)))
✓	99.5%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
	99.0%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
	98.2%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.0%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.1%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	56.7%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	98.2%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
✓	55.6%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
✓	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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))))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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))))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
▶	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
▶	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	98.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
▶	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))

Compiler

Compiled 2 115 to 1 383 computations (34.6% saved)

series70.0ms (0.7%)

Memory

7.9MiB live, 111.9MiB allocated; 50ms collecting garbage

Counts

57 → 292

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
(*.f64 (neg.f64 eps) #s(approx (sin x) x))
(neg.f64 eps)
#s(approx (sin x) x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))
(.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps)
(fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x))
(-.f64 (.f64 (.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 x eps) #s(literal 1/6 binary64))
(*.f64 x eps)
#s(literal 1/6 binary64)
(neg.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
(.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps)
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
(fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
(-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)
#s(literal 1/4 binary64)
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
#s(literal 1 binary64)
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))

Outputs
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))))
#s(approx (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))))
#s(approx (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 1))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (* 2 x) 1/2) #s(hole binary64 x))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (cos (* 1/2 eps)))))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps))))))))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 x))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (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))))))
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#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
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#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
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#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
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#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
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#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (- eps (* -2 x))))))
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#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
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#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (sin x)))
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#s(approx (cos (* 1/2 eps)) #s(hole binary64 1))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* -1/8 (pow eps 2)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))))
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#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1/6 (/ x eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/48 x) (* 1/6 (/ 1 eps)))))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* 1/4 (/ x eps))) eps)) (* 1/48 x))))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/4 x) (/ 1 eps)) eps))) eps)) (* 1/48 x))))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/48 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* 1/4 (/ x eps))) eps)) (* 1/48 x))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))))

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	eps	@	0	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) (- (* (* x eps) 1/6) 1/2) (* (* x eps) 1/6) (* x eps) 1/6 (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) x) (+ (* -1/48 (* eps eps)) 1/4) -1/48 (* eps eps) 1/4 (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2))
9.0ms	x	@	0	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) (- (* (* x eps) 1/6) 1/2) (* (* x eps) 1/6) (* x eps) 1/6 (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) x) (+ (* -1/48 (* eps eps)) 1/4) -1/48 (* eps eps) 1/4 (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2))
8.0ms	x	@	inf	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) (- (* (* x eps) 1/6) 1/2) (* (* x eps) 1/6) (* x eps) 1/6 (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) x) (+ (* -1/48 (* eps eps)) 1/4) -1/48 (* eps eps) 1/4 (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2))
7.0ms	x	@	-inf	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) (- (* (* x eps) 1/6) 1/2) (* (* x eps) 1/6) (* x eps) 1/6 (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) x) (+ (* -1/48 (* eps eps)) 1/4) -1/48 (* eps eps) 1/4 (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2))
7.0ms	eps	@	-inf	((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) (- (* (* x eps) 1/6) 1/2) (* (* x eps) 1/6) (* x eps) 1/6 (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) x) (+ (* -1/48 (* eps eps)) 1/4) -1/48 (* eps eps) 1/4 (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2))

rewrite259.0ms (2.8%)

Memory

-24.5MiB live, 248.3MiB allocated; 58ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1120	9503
0	1190	8789
1	6357	8771
0	8271	8439

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

349 → 533

Calls

Call 1

Inputs
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
(*.f64 (neg.f64 eps) #s(approx (sin x) x))
(neg.f64 eps)
#s(approx (sin x) x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps)))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))
(.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps)
(fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x))
(-.f64 (.f64 (.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 x eps) #s(literal 1/6 binary64))
(*.f64 x eps)
#s(literal 1/6 binary64)
(neg.f64 x)
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#s(literal -1/48 binary64)
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#s(literal 1/4 binary64)
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#s(approx (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))))
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#s(approx (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 1))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (* 2 x) 1/2) #s(hole binary64 x))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (cos (* 1/2 eps)))))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps))))))))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 x))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (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 (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
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#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (* x eps) 1/6) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* x eps) 1/6) 1/2) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (* (* x eps) 1/6) #s(hole binary64 (* 1/6 (* eps x))))
#s(approx (* x eps) #s(hole binary64 (* eps x)))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
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#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
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#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
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#s(approx (* (+ (* -1/48 (* eps eps)) 1/4) x) #s(hole binary64 (* x (+ 1/4 (* -1/48 (pow eps 2))))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (pow (sin (* 1/2 eps)) 2)))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))))
#s(approx (* (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
#s(approx (+ (* (sin (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (cos x)))
#s(approx (* (cos (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin x))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (sin x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
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#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))))
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#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* 1/24 (pow eps 4))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* 1/6 (/ x eps))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (* 1/6 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (* 1/6 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) #s(hole binary64 (* 1/6 (* (pow eps 3) x))))
#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) #s(hole binary64 (* (pow eps 3) (- (* 1/6 x) (* 1/2 (/ 1 eps))))))
#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) #s(hole binary64 (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) #s(hole binary64 (* 1/6 (* (pow eps 2) x))))
#s(approx (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) #s(hole binary64 (* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))))
#s(approx (- (* (* x eps) 1/6) 1/2) #s(hole binary64 (* eps (- (* 1/6 x) (* 1/2 (/ 1 eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (+ 1/24 (* -1/48 (pow x 2))))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (+ 1/24 (+ (* -1/48 (pow x 2)) (* 1/6 (/ x eps)))))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (+ (* -1/48 (pow x 2)) (+ (* 1/6 (/ x eps)) (* 1/4 (/ (pow x 2) (pow eps 2)))))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (+ (* -1 (/ x (pow eps 3))) (+ (* -1/48 (pow x 2)) (+ (* 1/6 (/ x eps)) (* 1/4 (/ (pow x 2) (pow eps 2))))))) (/ 1/2 (pow eps 2))))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* -1/48 (* (pow eps 3) x))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 3) (+ (* -1/48 x) (* 1/6 (/ 1 eps))))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 3) (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))) (/ 1 (pow eps 3))))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) #s(hole binary64 (* -1/48 (* (pow eps 3) x))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow eps 3) (+ (* -1/48 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) #s(hole binary64 (* (pow eps 3) (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/4) x) #s(hole binary64 (* -1/48 (* (pow eps 2) x))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/4) x) #s(hole binary64 (* (pow eps 2) (+ (* -1/48 x) (* 1/4 (/ x (pow eps 2)))))))
#s(approx (+ (* -1/48 (* eps eps)) 1/4) #s(hole binary64 (* -1/48 (pow eps 2))))
#s(approx (+ (* -1/48 (* eps eps)) 1/4) #s(hole binary64 (* (pow eps 2) (- (* 1/4 (/ 1 (pow eps 2))) 1/48))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/48 (pow eps 3))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* -1/48 (pow eps 2))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/6 x) (* 1/2 (/ 1 eps))) eps))))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x)) eps))))))
#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))))
#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))))
#s(approx (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))))
#s(approx (- (* (* x eps) 1/6) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/48 (pow x 2)) 1/24)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1/6 (/ x eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps))) eps)) (* 1/6 x)) eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/48 x) (* 1/6 (/ 1 eps)))))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* 1/4 (/ x eps))) eps)) (* 1/48 x))))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/4 x) (/ 1 eps)) eps))) eps)) (* 1/48 x))))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/48 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/6 (* 1/4 (/ x eps))) eps)) (* 1/48 x))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))))

Outputs
(.f64 #s(literal -2 binary64) #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (-.f64 (.f64 (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))))
(fma.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(sin.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(-.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64))) (sin.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
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#s(approx (* (* 2 x) 1/2) x)
#s(approx (* 2 x) (*.f64 #s(literal 2 binary64) x))
#s(approx x x)
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#s(approx (sin (* (* 2 x) 1/2)) x)
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#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))
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#s(approx (sin x) x)
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#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
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#s(approx (- (* (* x eps) 1/6) 1/2) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) (.f64 (*.f64 x x) #s(literal -1/48 binary64))) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64)) (fma.f64 (/.f64 (.f64 x x) (.f64 eps eps)) #s(literal 1/4 binary64) (.f64 (/.f64 x eps) #s(literal 1/6 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (+.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 (neg.f64 x) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (.f64 x x) #s(literal -1/48 binary64) (fma.f64 (/.f64 (.f64 x x) (.f64 eps eps)) #s(literal 1/4 binary64) (.f64 (/.f64 x eps) #s(literal 1/6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal -1/48 binary64)))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (*.f64 (fma.f64 #s(literal -1/48 binary64) x (/.f64 #s(literal 1/6 binary64) eps)) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (.f64 (fma.f64 #s(literal -1/48 binary64) x (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal 1/4 binary64) (/.f64 #s(literal 1/6 binary64) eps))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (.f64 (-.f64 (fma.f64 #s(literal -1/48 binary64) x (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal 1/4 binary64) (/.f64 #s(literal 1/6 binary64) eps))) (pow.f64 eps #s(literal -3 binary64))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal -1/48 binary64)))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (*.f64 (fma.f64 #s(literal -1/48 binary64) x (/.f64 #s(literal 1/6 binary64) eps)) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal -1/48 binary64) x (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal 1/4 binary64) (/.f64 #s(literal 1/6 binary64) eps))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/4) x) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/48 binary64)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/4) x) (.f64 (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal 1/4 binary64) (.f64 #s(literal -1/48 binary64) x)) (.f64 eps eps)))
#s(approx (+ (* -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))
#s(approx (+ (* -1/48 (* eps eps)) 1/4) (.f64 (-.f64 (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/48 binary64)) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))
#s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (*.f64 eps eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* 2 x) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/48 binary64)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps)))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) eps) #s(literal -1 binary64) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps))) eps) #s(literal -1 binary64) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) (neg.f64 (*.f64 (fma.f64 #s(literal -1/6 binary64) x (/.f64 #s(literal 1/2 binary64) eps)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (* (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) eps) (neg.f64 (*.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (- (* (* x eps) 1/6) 1/2) eps) (neg x)) (.f64 (fma.f64 #s(literal 1/6 binary64) x (neg.f64 (/.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) (.f64 eps eps)))
#s(approx (- (* (* x eps) 1/6) 1/2) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/6 binary64) x (/.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (neg.f64 (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) (-.f64 (.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/24 binary64))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (neg.f64 (.f64 (-.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) x (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64)) eps))) eps))) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (neg.f64 (.f64 (-.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) x (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (/.f64 x eps)) #s(literal 1/2 binary64)) eps))) eps))) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/48 binary64) x) (/.f64 #s(literal 1/6 binary64) eps)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (neg.f64 (*.f64 (fma.f64 #s(literal 1/48 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/4 binary64) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) (neg.f64 (*.f64 (fma.f64 #s(literal 1/48 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) x (pow.f64 eps #s(literal -1 binary64))) eps) #s(literal -1 binary64) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/48 binary64) x) (/.f64 #s(literal 1/6 binary64) eps)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (neg.f64 (*.f64 (fma.f64 #s(literal 1/48 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/4 binary64) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) (neg.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (* (sin (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 2 x) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (neg.f64 (.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 3 binary64)))))

eval84.0ms (0.9%)

Memory: 15.2MiB live, 115.8MiB allocated; 24ms collecting garbage
Compiler: Compiled 31 840 to 3 323 computations (89.6% saved)

prune46.0ms (0.5%)

Memory

1.5MiB live, 89.4MiB allocated; 14ms collecting garbage

Pruning

31 alts after pruning (25 fresh and 6 done)

	Pruned	Kept	Total
New	508	11	519
Fresh	7	14	21
Picked	3	2	5
Done	0	4	4
Total	518	31	549

Accuracy

100.0%

Counts

549 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 #s(approx (cos ( 1/2 eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 eps eps) #s(literal 1/384 binary64)) (.f64 eps eps)) #s(literal 1/8 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	99.8%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
	99.6%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
	99.4%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
	99.5%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
	99.5%	(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
✓	99.5%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
	99.0%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
	98.2%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
	98.1%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	56.7%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
	98.2%	#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
✓	55.6%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	99.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
✓	80.7%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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))))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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))))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
✓	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
✓	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
	79.9%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))

Compiler

Compiled 3 834 to 1 351 computations (64.8% saved)

regimes49.0ms (0.5%)

Memory

-23.4MiB live, 80.6MiB allocated; 15ms collecting garbage

Counts

61 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 #s(approx (cos ( 1/2 eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 eps eps) #s(literal 1/384 binary64)) (.f64 eps eps)) #s(literal 1/8 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64)))))

Outputs

(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (*.f64 #s(approx (cos (* 1/2 eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/46080 binary64) (*.f64 eps eps) #s(literal 1/384 binary64)) (*.f64 eps eps)) #s(literal 1/8 binary64)) (*.f64 eps eps) #s(literal 1 binary64))) (sin.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))

Calls

3 calls:

17.0ms	eps
13.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.8%	1	`x`
99.8%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.4%)

Memory

21.5MiB live, 65.5MiB allocated; 7ms collecting garbage

Counts

56 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))

Outputs

(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (fma.f64 #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))

Calls

3 calls:

13.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
12.0ms	x
12.0ms	eps

Results

Accuracy	Segments	Branch
99.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.8%	1	`x`
99.8%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.4%)

Memory

24.4MiB live, 68.9MiB allocated; 7ms collecting garbage

Counts

55 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

Calls

3 calls:

16.0ms	x
12.0ms	eps
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.7%	1	`x`
99.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes81.0ms (0.9%)

Memory

-121.2MiB live, 65.8MiB allocated; 62ms collecting garbage

Counts

54 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (fma.f64 (neg.f64 (sin.f64 x)) eps (.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

Outputs

(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))

Calls

3 calls:

52.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
14.0ms	eps
12.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.3%)

Memory

38.6MiB live, 38.6MiB allocated; 0ms collecting garbage

Counts

42 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Outputs

(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))

Calls

3 calls:

9.0ms	eps
9.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes37.0ms (0.4%)

Memory

-12.4MiB live, 34.2MiB allocated; 2ms collecting garbage

Counts

39 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))

Outputs

(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))

Calls

3 calls:

9.0ms	eps
9.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes80.0ms (0.9%)

Memory

-14.8MiB live, 31.2MiB allocated; 4ms collecting garbage

Counts

34 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx ( (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))

Outputs

(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))

Calls

3 calls:

65.0ms	x
8.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.4%)

Memory

-4.8MiB live, 39.0MiB allocated; 6ms collecting garbage

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))

Calls

3 calls:

20.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
7.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

33.1MiB live, 33.1MiB allocated; 0ms collecting garbage

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) eps) (sin.f64 x)) eps))

Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))

Calls

3 calls:

7.0ms	x
7.0ms	eps
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.4%)

Memory

-4.2MiB live, 45.4MiB allocated; 7ms collecting garbage

Counts

29 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) #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))) eps))

Calls

3 calls:

21.0ms	eps
7.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory

-4.8MiB live, 40.1MiB allocated; 5ms collecting garbage

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 #s(approx (- ( (* x eps) 1/6) 1/2) (.f64 (.f64 #s(literal 1/6 binary64) eps) x)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(approx (+ (* (* eps x) (- (* (* eps eps) 1/6) 1)) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x eps) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(approx (+ (* (- (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) 1) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #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 (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 #s(approx (+ (* (* (+ (* -1/48 (* eps eps)) 1/4) x) eps) (* (* eps eps) 1/6)) (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 #s(approx (+ ( -1/48 (* eps eps)) 1/4) (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))

Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (+ (* (* (cos x) eps) -1/2) (neg (sin x))) eps) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Calls

3 calls:

9.0ms	eps
6.0ms	x
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.2%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))

Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))

Calls

3 calls:

2.0ms	eps
2.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

-33.0MiB live, 11.7MiB allocated; 2ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) -1/2) (neg (sin x))) (*.f64 #s(literal -1/2 binary64) eps)) eps))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))

Calls

3 calls:

3.0ms	x
2.0ms	eps
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
79.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.9%	1	`x`
79.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

Calls

3 calls:

1.0ms	eps
1.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
55.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
55.6%	1	`x`
55.6%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations458.0ms (4.9%)

Memory

-4.7MiB live, 470.6MiB allocated; 69ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 560 to 164 computations (70.7% saved)

preprocess145.0ms (1.6%)

Memory: 15.1MiB live, 146.3MiB allocated; 20ms collecting garbage
Compiler: Compiled 1 194 to 390 computations (67.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze32.0ms (0.3%)

sample6.6s (71.1%)

explain199.0ms (2.1%)

preprocess99.0ms (1.1%)

series5.0ms (0%)

rewrite147.0ms (1.6%)

eval17.0ms (0.2%)

prune8.0ms (0.1%)

series41.0ms (0.4%)

rewrite201.0ms (2.2%)

eval53.0ms (0.6%)

prune27.0ms (0.3%)

series42.0ms (0.5%)

rewrite207.0ms (2.2%)

eval51.0ms (0.5%)

prune28.0ms (0.3%)

series70.0ms (0.7%)

rewrite259.0ms (2.8%)

eval84.0ms (0.9%)

prune46.0ms (0.5%)

regimes49.0ms (0.5%)

regimes41.0ms (0.4%)

regimes40.0ms (0.4%)

regimes81.0ms (0.9%)

regimes28.0ms (0.3%)

regimes37.0ms (0.4%)

regimes80.0ms (0.9%)

regimes36.0ms (0.4%)

regimes22.0ms (0.2%)

regimes34.0ms (0.4%)

regimes20.0ms (0.2%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes3.0ms (0%)

derivations458.0ms (4.9%)

preprocess145.0ms (1.6%)

end0.0ms (0%)

Profiling