Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

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

analyze33.0ms (0.4%)

Memory

1.7MiB live, 45.2MiB allocated; 7ms 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 (74.1%)

Memory

215.8MiB live, 5 916.7MiB allocated; 2.4s collecting garbage

Samples

2.7s	5 811×	2	valid
1.9s	26 352×	0	invalid
359.0ms	2 386×	1	valid
6.0ms	59×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.8s

ival-cos: 2.5s (66% of total)

adjust: 366.0ms (9.7% of total)

ival-fabs: 230.0ms (6.1% of total)

ival-sub!: 181.0ms (4.8% of total)

ival-add!: 163.0ms (4.3% of total)

ival-<: 132.0ms (3.5% of total)

ival-mult!: 129.0ms (3.4% of total)

ival-and: 66.0ms (1.8% of total)

ival-assert: 14.0ms (0.4% of total)

Bogosity

explain185.0ms (2.1%)

Memory

29.5MiB live, 220.2MiB allocated; 19ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
142	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	142	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	142	0
-	0	114

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	142	0	0
-	0	0	114

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	114
1	141
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

115.0ms	356×	2	valid
17.0ms	152×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-cos: 85.0ms (76% of total)

adjust: 19.0ms (17% of total)

ival-sub!: 6.0ms (5.4% of total)

ival-add!: 2.0ms (1.8% of total)

preprocess98.0ms (1.1%)

Memory

-36.1MiB live, 55.2MiB 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
▶	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 14 to 12 computations (14.3% saved)

series5.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB 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))

rewrite153.0ms (1.7%)

Memory

10.5MiB live, 193.4MiB allocated; 20ms 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 x (-.f64 x eps)) #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 x (-.f64 x eps)) #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 x (-.f64 x eps)) #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 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (cos.f64 x) (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))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.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))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))))))
(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 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 (cos.f64 x) (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))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))))))
(-.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))))))
(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)))
(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)))
(-.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 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (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 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 eps eps (.f64 x (-.f64 x eps))))
(-.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (.f64 (.f64 eps eps) (neg.f64 eps)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (.f64 (neg.f64 x) (.f64 x x)) (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 (.f64 (.f64 x x) x) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (.f64 (.f64 x x) x) (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
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(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 x (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 x (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (cos (+ x eps)) (cos.f64 eps))
#s(approx (cos (+ x eps)) (-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x)))
#s(approx (cos (+ x eps)) (fma.f64 x (-.f64 (.f64 (.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (cos (+ x eps)) (fma.f64 x (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) (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 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) 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 (-.f64 (/.f64 eps (neg.f64 x)) #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 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
#s(approx (cos (+ x eps)) (cos.f64 x))
#s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps)))
#s(approx (cos (+ x eps)) (fma.f64 eps (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 eps (-.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)) (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 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)) (neg.f64 eps)))

eval10.0ms (0.1%)

Memory: 20.8MiB live, 20.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 050 to 439 computations (78.6% saved)

prune12.0ms (0.1%)

Memory

-29.2MiB live, 17.6MiB allocated; 3ms 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

99.7%

Counts

107 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.0%	(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	48.4%	(-.f64 (cos.f64 (+.f64 x eps)) #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))))
▶	48.6%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64))))
▶	48.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶	77.2%	(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	50.2%	(.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)))))
▶	47.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	99.1%	#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))
▶	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 461 to 314 computations (31.9% saved)

series44.0ms (0.5%)

Memory

15.4MiB live, 67.9MiB allocated; 6ms collecting garbage

Counts

48 → 234

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))
(.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps))
(cos.f64 x)
x
#s(literal -1/2 binary64)
(.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(sin.f64 x)
#s(literal 1/6 binary64)
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (cos.f64 x) eps)
eps
#s(literal 1/24 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)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64)))
(fma.f64 (.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)) x) x #s(literal 1 binary64))
(.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)) x)
(-.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 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/2 binary64)
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))))
#s(literal -2 binary64)
(sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))
(-.f64 x (-.f64 x eps))
(-.f64 x eps)
#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)
(+.f64 eps 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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #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 (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x)))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/48 (* (pow eps 2) x)) (* 1/6 eps))))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 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 (* (* (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 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 x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 1))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* x (- (* 1/24 (pow x 2)) 1/2))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* -1/720 (pow x 2))))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* -2 (sin (* 1/2 eps)))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- x (- x eps)) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- x (- x eps)) #s(hole binary64 eps))
#s(approx (- x eps) #s(hole binary64 (* -1 eps)))
#s(approx (- x eps) #s(hole binary64 (- x eps)))
#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 (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (* 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 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 (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1/720 (pow x 5))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* -1/720 (pow x 3))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (- x eps) #s(hole binary64 x))
#s(approx (- x eps) #s(hole binary64 (* x (+ 1 (* -1 (/ eps 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 (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps 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 (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* x (- (/ eps x) 1)))))
#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 (+ eps x) #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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (* 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 (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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* -1 eps)))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/1920 (pow eps 2)))) 1))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/322560 (pow eps 2)) 1/1920)))) 1))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (- x eps) #s(hole binary64 (+ x (* -1 eps))))
#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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #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)) eps) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #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)) #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 (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- x eps) #s(hole binary64 (* eps (- (/ x eps) 1))))
#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 (+ eps x) #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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #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 (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ x 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)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (cos x) x -1/2 (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) eps 1/24 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (* (+ (* -1/720 (* x x)) 1/24) x) (+ (* -1/720 (* x x)) 1/24) -1/720 1/2 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) -2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) 2 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
8.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (cos x) x -1/2 (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) eps 1/24 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (* (+ (* -1/720 (* x x)) 1/24) x) (+ (* -1/720 (* x x)) 1/24) -1/720 1/2 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) -2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) 2 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
7.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (cos x) x -1/2 (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) eps 1/24 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (* (+ (* -1/720 (* x x)) 1/24) x) (+ (* -1/720 (* x x)) 1/24) -1/720 1/2 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) -2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) 2 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
6.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (cos x) x -1/2 (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) eps 1/24 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (* (+ (* -1/720 (* x x)) 1/24) x) (+ (* -1/720 (* x x)) 1/24) -1/720 1/2 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) -2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) 2 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
5.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (cos x) x -1/2 (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) eps 1/24 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) (- (cos (+ x eps)) (cos x)) (cos x) (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (* (+ (* -1/720 (* x x)) 1/24) x) (+ (* -1/720 (* x x)) 1/24) -1/720 1/2 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) -2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) 2 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))

rewrite226.0ms (2.5%)

Memory

-5.9MiB live, 206.3MiB allocated; 87ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	851	6004
0	915	5876
1	4649	5876
0	8133	5672

Stop Event

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

Counts

282 → 446

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))
(.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps))
(cos.f64 x)
x
#s(literal -1/2 binary64)
(.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(sin.f64 x)
#s(literal 1/6 binary64)
(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (cos.f64 x) eps)
eps
#s(literal 1/24 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)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64)))
(fma.f64 (.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)) x) x #s(literal 1 binary64))
(.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)) x)
(-.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 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x)
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
#s(literal 1/2 binary64)
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))))
#s(literal -2 binary64)
(sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))
(-.f64 x (-.f64 x eps))
(-.f64 x eps)
#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)
(+.f64 eps 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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #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 (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x)))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (+ (* 1/24 (pow eps 2)) (* x (+ (* -1/48 (* (pow eps 2) x)) (* 1/6 eps))))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 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 (* (* (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 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 x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 1))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* x (- (* 1/24 (pow x 2)) 1/2))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* -1/720 (pow x 2))))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* -2 (sin (* 1/2 eps)))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- x (- x eps)) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- x (- x eps)) #s(hole binary64 eps))
#s(approx (- x eps) #s(hole binary64 (* -1 eps)))
#s(approx (- x eps) #s(hole binary64 (- x eps)))
#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 (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (* 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 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 (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* -1/720 (pow x 6))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1/720 (pow x 5))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* -1/720 (pow x 4))))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* -1/720 (pow x 3))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* -1/720 (pow x 2))))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (- x eps) #s(hole binary64 x))
#s(approx (- x eps) #s(hole binary64 (* x (+ 1 (* -1 (/ eps 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 (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps 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 (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* x (- (/ eps x) 1)))))
#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 (+ eps x) #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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #s(hole binary64 (* 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 (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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* -1 eps)))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/1920 (pow eps 2)))) 1))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/322560 (pow eps 2)) 1/1920)))) 1))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (- x eps) #s(hole binary64 (+ x (* -1 eps))))
#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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #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)) eps) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) #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)) #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 (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- x eps) #s(hole binary64 (* eps (- (/ x eps) 1))))
#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 (+ eps x) #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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) #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 (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ x 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)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (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))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (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))) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 (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))) eps) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (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))) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 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))) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (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))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (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))) eps) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 (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))) eps) (sin.f64 x)))))
(-.f64 (.f64 (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))) eps) (sin.f64 x))
(.f64 (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))) eps)
(.f64 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))))
(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)))
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#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (-.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 (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 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))
#s(approx x x)
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1/24 binary64))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/48 binary64) (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal 1/24 binary64))))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps x) #s(literal -1/36 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps))) x (.f64 #s(literal 1/6 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 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 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (* (* (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 (.f64 x x) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/48 binary64) eps)) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* (* (cos x) eps) 1/24) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/17280 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/576 binary64) eps)) (.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 (.f64 x x) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#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 x (-.f64 (.f64 (.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (cos (+ x eps)) (fma.f64 x (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) x) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (+ (* (* x x) -1/2) 1) #s(literal 1 binary64))
#s(approx (+ (* (* x x) -1/2) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) #s(literal 1 binary64))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (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 (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (fma.f64 (.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (-.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) x))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (*.f64 #s(literal 1/24 binary64) x))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x))
#s(approx (+ (* -1/720 (* x x)) 1/24) #s(literal 1/24 binary64))
#s(approx (+ (* -1/720 (* x x)) 1/24) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.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)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) x)) x (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (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))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) 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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
#s(approx (sin (/ (- x (- x eps)) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (/ (- x (- x eps)) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- x (- x eps)) eps)
#s(approx (- x eps) (neg.f64 eps))
#s(approx (- x eps) (-.f64 x eps))
#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 x (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 x (fma.f64 x (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal -1/6 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (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 (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (-.f64 (.f64 (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))) eps) (sin.f64 x)) eps))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (-.f64 (.f64 (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))) eps) (sin.f64 x)))
#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (.f64 (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))) eps))
#s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) 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))))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps))
#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 eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) #s(literal -1/720 binary64)))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (-.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/720 binary64)))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/720 binary64)))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64))))
#s(approx (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x))))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/720 binary64)))
#s(approx (* (* (+ (* -1/720 (* x x)) 1/24) x) x) (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 (.f64 (*.f64 x x) x) #s(literal -1/720 binary64)))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 (.f64 (.f64 x x) x) (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64))))
#s(approx (+ (* -1/720 (* x x)) 1/24) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
#s(approx (+ (* -1/720 (* x x)) 1/24) (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/720 binary64)) (*.f64 x x)))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- x eps) x)
#s(approx (- x eps) (*.f64 (+.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)) x))
#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 x x))
#s(approx (+ (+ eps x) x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (neg.f64 (.f64 (-.f64 #s(literal 1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (- (* (* (+ (* -1/720 (* x x)) 1/24) x) x) 1/2) x) (neg.f64 (.f64 (+.f64 #s(literal 1/720 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (+ (* -1/720 (* x x)) 1/24) x) (.f64 (.f64 (neg.f64 x) (.f64 x x)) (-.f64 #s(literal 1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 eps x) #s(literal 1 binary64))))
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#s(approx eps eps)
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#s(approx (- (cos eps) 1) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))
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#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)))
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#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps))) (cos.f64 x)))
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#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 eps eps) eps)) (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 (.f64 eps eps) (.f64 eps eps))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps)) #s(literal 1/24 binary64)))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) eps) (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))))))
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#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps)) #s(literal 1/24 binary64)))
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#s(approx (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (.f64 (.f64 (.f64 eps eps) eps) (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 (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (.f64 (.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal 1/24 binary64)))
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#s(approx (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (.f64 (.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal 1/24 binary64)))
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#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 (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
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#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 (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
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#s(approx (- x eps) (*.f64 (neg.f64 eps) (+.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
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#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval61.0ms (0.7%)

Memory: 9.4MiB live, 102.9MiB allocated; 10ms collecting garbage
Compiler: Compiled 16 221 to 2 714 computations (83.3% saved)

prune24.0ms (0.3%)

Memory

-7.4MiB live, 38.9MiB allocated; 3ms collecting garbage

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	465	16	481
Fresh	3	3	6
Picked	5	0	5
Done	0	1	1
Total	473	20	493

Accuracy

100.0%

Counts

493 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	48.4%	(-.f64 (cos.f64 (+.f64 x eps)) #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))))
	77.2%	(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))))
▶	99.5%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.5%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	98.9%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (neg.f64 eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
▶	47.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.1%	#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))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 #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))) eps)) eps) (sin.f64 x)) eps))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
▶	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	96.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
	96.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
	35.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (.f64 (neg.f64 (.f64 (*.f64 eps eps) eps)) (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 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) eps))))) eps))
	49.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
▶	96.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)))))
	96.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)))))
▶	99.7%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))

Compiler

Compiled 1 435 to 950 computations (33.8% saved)

series44.0ms (0.5%)

Memory

-36.6MiB live, 62.3MiB allocated; 8ms collecting garbage

Counts

49 → 223

Calls

Call 1

Inputs
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (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)) #s(literal -2 binary64)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
#s(literal -2 binary64)
(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
#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)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))))
(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)))
(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))
(.f64 (.f64 eps eps) x)
(*.f64 eps eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))
#s(literal -1/48 binary64)
#s(literal 1/4 binary64)
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
#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)
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)
(-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1 binary64))
(.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps))
(fma.f64 #s(literal -1/1920 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))
#s(literal -1/1920 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)
(+.f64 eps x)

Outputs
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #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 (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #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 (* (+ (* 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 (* (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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* 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) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* 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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps 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 (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* eps (- (* 1/6 (pow eps 2)) 1))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
#s(approx (* (* eps eps) x) #s(hole binary64 (* (pow eps 2) x)))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* -2 (sin (* 1/2 eps)))))
#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 (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))))
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#s(approx (cos eps) #s(hole binary64 1))
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#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
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#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 (+ 1/24 (* -1/1920 (pow eps 2)))))
#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))))))
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#s(approx (* (sin (* 1/2 eps)) -2) #s(hole binary64 (* -2 (sin (* 1/2 eps)))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#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))))))
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#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 (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1/1920 (pow eps 5))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4)))))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* -1/1920 (pow eps 4))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4)))))))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) #s(hole binary64 (* -1/1920 (pow eps 4))))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) #s(hole binary64 (* (pow eps 4) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 (* -1/1920 (pow eps 2))))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#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 (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* -2 (* (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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1/4 (/ x eps)) 1/6) eps)) (* -1/48 x)))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (- (* 1/4 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/48 x)))))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- 1/1920 (* 1/24 (/ 1 (pow eps 2))))))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2))))))))
#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)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) (+ (* -1/1920 (* eps eps)) 1/24) -1/1920 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
7.0ms	x	@	inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) (+ (* -1/1920 (* eps eps)) 1/24) -1/1920 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
6.0ms	eps	@	inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) (+ (* -1/1920 (* eps eps)) 1/24) -1/1920 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
5.0ms	eps	@	-inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) (+ (* -1/1920 (* eps eps)) 1/24) -1/1920 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
4.0ms	eps	@	0	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1/6 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* -2 (sin (/ (- x (- x eps)) 2))) (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) (+ (* -1/1920 (* eps eps)) 1/24) -1/1920 (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))

rewrite179.0ms (2%)

Memory

46.9MiB live, 229.9MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	835	6325
0	899	6111
1	4599	6109
0	8022	5932

Stop Event

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

Counts

272 → 418

Calls

Call 1

Inputs
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (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)) #s(literal -2 binary64)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
#s(literal -2 binary64)
(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
#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)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))))
(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)))
(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))
(.f64 (.f64 eps eps) x)
(*.f64 eps eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))
#s(literal -1/48 binary64)
#s(literal 1/4 binary64)
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
#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)
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)
(-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1 binary64))
(.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps))
(fma.f64 #s(literal -1/1920 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))
#s(literal -1/1920 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)
(+.f64 eps x)
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (pow (sin (* 1/2 eps)) 2))))
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#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
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#s(approx x #s(hole binary64 x))
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#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
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#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 (* (* eps eps) x) #s(hole binary64 (* (pow eps 2) x)))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* -2 (sin (* 1/2 eps)))))
#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))))))
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#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 (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps 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))
#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 (* (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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 2) (* (pow x 2) (+ 1/4 (* -1/48 (pow eps 2)))))))
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#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (+ (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* x (+ (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) 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 (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 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 (* -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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))) (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) 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 (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 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 (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #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 (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #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 (* 1/2 eps)) -2) #s(hole binary64 (* -1 eps)))
#s(approx (* (sin (* 1/2 eps)) -2) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1))))
#s(approx (* (sin (* 1/2 eps)) -2) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/1920 (pow eps 2)))) 1))))
#s(approx (* (sin (* 1/2 eps)) -2) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/322560 (pow eps 2)) 1/1920)))) 1))))
#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 eps #s(hole binary64 eps))
#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 (- (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 (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* -1 (* eps x))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* eps (- (+ (* 1/6 (* eps x)) (* 1/4 (pow x 2))) 1/2))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* eps (+ (* -1 x) (* eps (- (+ (* 1/4 (pow x 2)) (* eps (+ (* 1/6 x) (* eps (+ 1/24 (* -1/48 (pow x 2))))))) 1/2))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* eps (- (* 1/4 (* eps x)) 1))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* eps (- (* eps (+ (* 1/6 eps) (* 1/4 x))) 1))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* eps (- (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/48 (* eps x)))))) 1))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* -1/48 (* eps eps)) 1/4) #s(hole binary64 1/4))
#s(approx (+ (* -1/48 (* eps eps)) 1/4) #s(hole binary64 (+ 1/4 (* -1/48 (pow eps 2)))))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) #s(hole binary64 (* eps (- (* 1/6 (pow eps 2)) 1))))
#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) 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 (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* -1 eps)))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/1920 (pow eps 2)))) 1))))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/322560 (pow eps 2)) 1/1920)))) 1))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/24 (* -1/1920 (pow eps 2)))) 1))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 -1))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1)))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (- (* (pow eps 2) (+ 1/24 (* -1/1920 (pow eps 2)))) 1)))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1/24 (* -1/1920 (pow eps 2))))))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 (+ 1/24 (* -1/1920 (pow eps 2)))))
#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 (* 1/2 eps)) -2) #s(hole binary64 (* -2 (sin (* 1/2 eps)))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#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 (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1/48 (pow x 2))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1/48 (pow x 2)) (* 1/6 (/ x eps)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 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 (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 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 (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* -1/48 (* (pow eps 4) x))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1/48 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1/48 x) (+ (* 1/4 (/ x (pow eps 2))) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -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) #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) 1/6) 1) eps) #s(hole binary64 (* 1/6 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) #s(hole binary64 (* (pow eps 3) (- 1/6 (/ 1 (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 (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1/1920 (pow eps 5))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4)))))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* -1/1920 (pow eps 4))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4)))))))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) #s(hole binary64 (* -1/1920 (pow eps 4))))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) #s(hole binary64 (* (pow eps 4) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 (* -1/1920 (pow eps 2))))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920))))
#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 (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* -2 (* (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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 x)) eps)) (* -1/48 (pow x 2)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1/4 (/ x eps)) 1/6) eps)) (* -1/48 x)))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (- (* 1/4 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/48 x)))))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- 1/1920 (* 1/24 (/ 1 (pow eps 2))))))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2))))))))
#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)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Outputs
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(exp.f64 (.f64 (log.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
#s(literal -2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (+.f64 x 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 x x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x 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 x x)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal -2 binary64)) (.f64 x #s(literal -2 binary64)))) (+.f64 eps (*.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal -8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (fma.f64 (.f64 x #s(literal -2 binary64)) (.f64 x #s(literal -2 binary64)) (.f64 eps (*.f64 x #s(literal -2 binary64))))))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps (+.f64 x x)))))
(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps))))
(/.f64 (fma.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (.f64 (.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 (+.f64 eps x) x))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 x #s(literal -2 binary64)))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (+.f64 x x))
(+.f64 x (+.f64 eps x))
#s(literal 2 binary64)
x
#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 (.f64 (.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(approx (cos eps) #s(literal 1 binary64))) #s(approx (cos eps) #s(literal 1 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)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(.f64 (.f64 (sin.f64 x) eps) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (sin.f64 x) eps))
(*.f64 (sin.f64 x) (neg.f64 eps))
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(fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -1/1920 binary64))))
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(fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -1/1920 binary64))))
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(fma.f64 (*.f64 #s(literal -1/1920 binary64) eps) eps #s(literal 1/24 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/1920 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal -1/1920 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))
(-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)))
(+.f64 (.f64 (.f64 eps eps) #s(literal -1/1920 binary64)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) #s(literal -1/1920 binary64)))
#s(literal -1/1920 binary64)
(sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #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)))))
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(/.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)))
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(/.f64 (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
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(/.f64 (fma.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (.f64 (.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 (+.f64 eps x) x))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 x #s(literal -2 binary64)))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 eps x) x)
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(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 eps eps (-.f64 (.f64 x x) (*.f64 eps x))))
(+.f64 eps x)
(+.f64 x eps)
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#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (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))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) 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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (.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)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) x)) x (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (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))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) 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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.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 x (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (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 x (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 x (-.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)) (cos.f64 eps)) #s(literal 1 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 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 eps x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) (.f64 eps eps))) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #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)))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* 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) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* 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 eps x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) (.f64 eps eps))) x (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) (.f64 eps eps))))
#s(approx (* (* eps eps) x) (.f64 (.f64 eps eps) x))
#s(approx (* -2 (sin (/ (- x (- x eps)) 2))) (.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 x (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (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 (+ (* 2 x) eps) eps)
#s(approx (+ (* 2 x) eps) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (.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) (fma.f64 #s(literal 2 binary64) x eps))))
#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 x 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 eps x)) (cos.f64 x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
#s(approx (sin x) (sin.f64 x))
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#s(approx (cos eps) #s(literal 1 binary64))
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#s(approx (sin (/ (+ (+ eps x) x) 2)) (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps)) (sin.f64 x)))
#s(approx (* (sin (* 1/2 eps)) -2) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
#s(approx (sin (* 1/2 eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) 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 (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (.f64 (.f64 eps eps) eps)) (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 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/24 binary64))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps 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)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps 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))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (+.f64 (+.f64 (/.f64 (neg.f64 x) (.f64 (.f64 eps eps) eps)) (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))))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) x) #s(literal -1/48 binary64)))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) x (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.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))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.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))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) eps))) (.f64 (.f64 eps eps) (*.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 #s(literal 1/4 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/6 binary64)))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) (.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) eps)))
#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) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #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))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#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 (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/1920 binary64)))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (pow.f64 eps #s(literal 5 binary64))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal -1/1920 binary64)))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal -1/1920 binary64)))
#s(approx (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) (.f64 (.f64 eps eps) #s(literal -1/1920 binary64)))
#s(approx (+ (* -1/1920 (* eps eps)) 1/24) (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (*.f64 eps eps)))
#s(approx (/ (+ (+ eps x) x) 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 (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64)))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64)))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (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))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps))) eps))) #s(literal 1/24 binary64)) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (/.f64 (neg.f64 x) eps)) #s(literal 1/2 binary64)) eps))) eps))) #s(literal 1/24 binary64)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 #s(literal -1/4 binary64) (/.f64 x eps)) #s(literal 1/6 binary64)) eps))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) x (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1 binary64) eps)) eps)) #s(literal 1/6 binary64)) eps))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) (.f64 (.f64 (.f64 eps eps) (neg.f64 eps)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (neg.f64 (.f64 (-.f64 #s(literal 1/1920 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64)))))
#s(approx (* (- (* (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (neg.f64 (.f64 (+.f64 #s(literal 1/1920 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64)))))
#s(approx (sin (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 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 (+ (* 2 x) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval77.0ms (0.9%)

Memory: 4.4MiB live, 140.6MiB allocated; 36ms collecting garbage
Compiler: Compiled 25 186 to 2 535 computations (89.9% saved)

prune37.0ms (0.4%)

Memory

-5.0MiB live, 40.4MiB allocated; 10ms collecting garbage

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	440	17	457
Fresh	5	9	14
Picked	3	2	5
Done	0	1	1
Total	448	29	477

Accuracy

100.0%

Counts

477 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	48.4%	(-.f64 (cos.f64 (+.f64 x eps)) #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))))
	99.5%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	24.2%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 #s(approx (- ( (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps eps)))) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	98.9%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (neg.f64 eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
✓	47.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.1%	#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))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 #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))) eps)) eps) (sin.f64 x)) eps))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
✓	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	79.4%	#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))))
▶	79.1%	#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))))
	78.9%	#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))))
▶	78.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
	96.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
	35.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (.f64 (neg.f64 (.f64 (*.f64 eps eps) eps)) (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 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) eps))))) eps))
	49.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	96.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps) #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)))))
	96.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (neg.f64 eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
▶	96.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) (neg.f64 (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))) x))) (.f64 x x)))))
	96.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
	96.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
	48.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x))))))
	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)))
▶	99.7%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
	95.7%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (exp.f64 (.f64 (log.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64))) #s(literal -2 binary64)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
	99.4%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
▶	98.9%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))

Compiler

Compiled 2 544 to 1 609 computations (36.8% saved)

series46.0ms (0.5%)

Memory

9.8MiB live, 56.6MiB allocated; 3ms collecting garbage

Counts

54 → 249

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	-inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 1/2 eps) x) x (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (* x x)) (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (+ (* (* eps eps) -1/48) 1/4) (* eps eps) -1/48 1/4 (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x))) (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)) (/ (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24)
7.0ms	eps	@	inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 1/2 eps) x) x (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (* x x)) (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (+ (* (* eps eps) -1/48) 1/4) (* eps eps) -1/48 1/4 (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x))) (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)) (/ (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24)
6.0ms	x	@	inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 1/2 eps) x) x (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (* x x)) (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (+ (* (* eps eps) -1/48) 1/4) (* eps eps) -1/48 1/4 (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x))) (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)) (/ (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24)
6.0ms	eps	@	-inf	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 1/2 eps) x) x (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (* x x)) (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (+ (* (* eps eps) -1/48) 1/4) (* eps eps) -1/48 1/4 (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x))) (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)) (/ (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24)
5.0ms	x	@	0	((* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps -2 (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 1/2 eps) x) x (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (* (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (* x x)) (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (+ (* (* eps eps) -1/48) 1/4) (* eps eps) -1/48 1/4 (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x))) (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)) (/ (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24)

rewrite234.0ms (2.6%)

Memory

-14.8MiB live, 172.2MiB allocated; 59ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1060	10075
0	1123	9662
1	6216	9662
0	8640	9331

Stop Event

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

Counts

303 → 457

Calls

Call 1

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

Outputs
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -2 binary64) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (sin.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
#s(literal -2 binary64)
(sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps)) (.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps))) (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps) (-.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 eps eps) eps))) (fma.f64 x x (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps)) (.f64 x (.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
(-.f64 x (*.f64 #s(literal -1/2 binary64) eps))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (sin x) x) (neg.f64 eps)))
(*.f64 #s(approx (sin x) x) (neg.f64 eps))
(*.f64 (neg.f64 eps) #s(approx (sin x) x))
(neg.f64 (*.f64 eps #s(approx (sin x) x)))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 eps #s(literal -1 binary64))
(neg.f64 eps)
#s(approx (sin x) x)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 eps)))
(.f64 #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) (neg.f64 eps))
(.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(neg.f64 (.f64 eps #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
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(fma.f64 #s(literal -1 binary64) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 eps) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))
(fma.f64 (neg.f64 eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))
(-.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 eps)) (.f64 #s(literal 1 binary64) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) (.f64 eps eps))))
(-.f64 (.f64 (neg.f64 (.f64 eps eps)) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(+.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 eps)) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))
(+.f64 (.f64 (neg.f64 (.f64 eps eps)) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 eps)))
(/.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 (.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 eps eps) eps))) #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 (neg.f64 (.f64 eps eps)) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
(.f64 (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) (*.f64 eps eps)) #s(literal -1 binary64))
(.f64 (.f64 eps eps) (neg.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) x)
(neg.f64 (.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) (.f64 eps eps)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) (.f64 eps eps))
(.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))
(.f64 eps (.f64 eps (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (neg.f64 x))
(/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) x)
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)) (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) x))) (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)) (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (neg.f64 x))
(/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1/24 binary64) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
(-.f64 (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.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 eps #s(literal 1/24 binary64)))
#s(literal 1/24 binary64)
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.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)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) x)) x (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (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))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) 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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (.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)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) x)) x (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (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))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))) 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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.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 x (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (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 (+ (* 1/2 eps) x) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (* 1/2 eps) x) (fma.f64 #s(literal 1/2 binary64) eps x))
#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 x (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 x (-.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)) (cos.f64 eps)) #s(literal 1 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 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/120 binary64) eps)) (.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#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 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(literal 1 binary64))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64))
#s(approx (- (* 1/120 (* x x)) 1/6) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
#s(approx (* 1/120 (* x x)) (.f64 (.f64 x x) #s(literal 1/120 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* 2 x) eps) eps)
#s(approx (+ (* 2 x) eps) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 eps x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) (.f64 eps eps) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x)))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) eps) eps (.f64 (.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x)))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* 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))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 eps x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* 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 (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) (.f64 eps eps) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x)))
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#s(approx (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps x)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 eps eps))) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps x)) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (*.f64 x x)) #s(literal -1/24 binary64)))
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#s(approx (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 eps x))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 eps eps) eps) x)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (.f64 x x)))) (/.f64 #s(literal 1/6 binary64) (.f64 eps x))) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) x) #s(literal -1/24 binary64)))
#s(approx (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (neg.f64 (.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) eps) (/.f64 #s(literal 1/24 binary64) x)) (.f64 (.f64 eps eps) (.f64 eps eps)))))
#s(approx (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) x)) (/.f64 #s(literal 1/24 binary64) x)) (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) eps)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) x))) (/.f64 #s(literal 1/24 binary64) x)) (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#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) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (*.f64 eps eps)))
#s(approx (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) x) #s(literal -1/24 binary64)))
#s(approx (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) x)) (/.f64 #s(literal 1/24 binary64) x)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)) (.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) x) #s(literal 1/24 binary64)))
#s(approx (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)) (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) x))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (/ (- (* (* eps eps) 1/24) 1/2) x) (.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/24 binary64)))
#s(approx (/ (- (* (* eps eps) 1/24) 1/2) x) (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) x))) (.f64 eps eps)))
#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 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64)))))
#s(approx (* (* (sin (* 1/2 eps)) -2) (sin (* (+ (* 2 x) eps) 1/2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64)))))
#s(approx (sin (* (+ (* 2 x) eps) 1/2)) (sin.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 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 (+ (* 1/2 eps) x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))
#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) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (.f64 (fma.f64 (cos.f64 x) #s(literal 1/24 binary64) (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))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps))) eps))) #s(literal 1/24 binary64)) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/48 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (/.f64 (neg.f64 x) eps)) #s(literal 1/2 binary64)) eps))) eps))) #s(literal 1/24 binary64)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (* (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (* x x)) (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (.f64 (.f64 x x) (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps)))) eps))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (* x x)) (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) x (neg.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x x) (/.f64 (neg.f64 x) eps)) eps))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps)) (/.f64 #s(literal 1/6 binary64) x)) eps)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) #s(literal 1/48 binary64)) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 eps x))) eps)) (/.f64 #s(literal 1/6 binary64) x)) eps)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) #s(literal 1/48 binary64)) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) eps)) (/.f64 #s(literal 1/6 binary64) x)) eps)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x)) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) eps)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) x)) (/.f64 #s(literal 1/6 binary64) x))) eps)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) x) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) eps))) eps)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x) (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps x)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps)) (/.f64 #s(literal 1/6 binary64) x)) eps)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x))) eps)) (/.f64 #s(literal 1/24 binary64) x))))
#s(approx (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) #s(literal 1/6 binary64)) eps)) (/.f64 #s(literal 1/24 binary64) x)) (.f64 (.f64 eps eps) (.f64 eps eps))))

eval61.0ms (0.7%)

Memory: 26.2MiB live, 71.1MiB allocated; 4ms collecting garbage
Compiler: Compiled 41 885 to 3 500 computations (91.6% saved)

prune45.0ms (0.5%)

Memory

-3.3MiB live, 48.6MiB allocated; 7ms collecting garbage

Pruning

34 alts after pruning (28 fresh and 6 done)

	Pruned	Kept	Total
New	469	10	479
Fresh	3	18	21
Picked	2	3	5
Done	0	3	3
Total	474	34	508

Accuracy

100.0%

Counts

508 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	99.5%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	24.2%	(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 #s(approx (- ( (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps eps)))) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
✓	47.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.1%	#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))
	99.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 #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))) eps)) eps) (sin.f64 x)) eps))
	98.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
✓	80.3%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	79.4%	#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))))
	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))))
	78.9%	#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))))
	34.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 x x))) (.f64 x x) #s(literal 1 binary64)) x))))
	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))) x))))
	48.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 #s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))) x))))
✓	78.6%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
	97.2%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
	96.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
	35.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (.f64 (neg.f64 (.f64 (*.f64 eps eps) eps)) (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 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) eps))))) eps))
	49.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	96.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps) #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)))))
	96.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (neg.f64 eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))))
	96.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
	96.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)) eps))))
	48.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x))))))
	78.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))
	51.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) eps)) (.f64 x x)))))
	79.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)))
✓	99.7%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
	95.7%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (exp.f64 (.f64 (log.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64))) #s(literal -2 binary64)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
	99.6%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/322560 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
	99.4%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
✓	98.9%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
	98.9%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	98.8%	#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (.f64 #s(approx (+ ( 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))))

Compiler

Compiled 4 041 to 1 477 computations (63.4% saved)

regimes43.0ms (0.5%)

Memory

-7.7MiB live, 38.1MiB allocated; 3ms 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 (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))
#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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.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 (neg.f64 eps) #s(approx (sin x) (.f64 #s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (neg.f64 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 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))))
#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 (neg.f64 eps) #s(approx (sin x) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.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)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) eps)) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 x x))) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (neg.f64 eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (.f64 #s(approx (+ ( 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) (neg.f64 (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))) x))) (.f64 x x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/322560 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(-.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 (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 #s(approx (- ( (+ (* -1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps eps)))) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (exp.f64 (.f64 (log.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64))) #s(literal -2 binary64)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 #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))) eps)) eps) (sin.f64 x)) eps))
(.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)))))
#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 (cos.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (.f64 (neg.f64 (.f64 (*.f64 eps eps) eps)) (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 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) eps))))) eps))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.7%	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)

regimes33.0ms (0.4%)

Memory

-15.6MiB live, 30.3MiB allocated; 2ms collecting garbage

Counts

43 → 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 (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))
#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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.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 (neg.f64 eps) #s(approx (sin x) (.f64 #s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (neg.f64 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 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))))
#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 (neg.f64 eps) #s(approx (sin x) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.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)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) eps)) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 x x))) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (neg.f64 eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (.f64 #s(approx (+ ( 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) (neg.f64 (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))) x))) (.f64 x x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/322560 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(-.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 (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))

Outputs

#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (*.f64 #s(approx (* (sin (* 1/2 eps)) -2) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/322560 binary64) (*.f64 eps eps)) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))

Calls

3 calls:

13.0ms	x
10.0ms	eps
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)

regimes28.0ms (0.3%)

Memory

28.0MiB live, 28.0MiB allocated; 0ms 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 (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))
#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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.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 (neg.f64 eps) #s(approx (sin x) (.f64 #s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (neg.f64 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 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))))
#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 (neg.f64 eps) #s(approx (sin x) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.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)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) eps)) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 x x))) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (neg.f64 eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (.f64 #s(approx (+ ( 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) (neg.f64 (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))) x))) (.f64 x x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))

Outputs

(*.f64 #s(approx (* -2 (sin (/ (- x (- x eps)) 2))) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/1920 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))

Calls

3 calls:

9.0ms	x
9.0ms	eps
7.0ms	(-.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)

regimes30.0ms (0.3%)

Memory

-18.4MiB live, 27.7MiB allocated; 2ms collecting garbage

Counts

38 → 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 (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))
#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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.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 (neg.f64 eps) #s(approx (sin x) (.f64 #s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (neg.f64 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 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))))
#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 (neg.f64 eps) #s(approx (sin x) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.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)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) eps)) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 x x))) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (neg.f64 eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (.f64 #s(approx (+ ( 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx ( (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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))
(.f64 #s(approx ( -2 (sin (/ (- x (- x eps)) 2))) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/1920 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (.f64 eps eps) (neg.f64 (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (neg.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)))) x))) (.f64 x x)))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (.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)) x) x #s(literal 1 binary64))))

Outputs

(*.f64 #s(approx (* -2 (sin (/ (- x (- x eps)) 2))) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/1920 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1 binary64)) eps)) (sin.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))

Calls

3 calls:

12.0ms	eps
9.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.3%)

Memory

25.5MiB live, 25.5MiB allocated; 0ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.3%)

Memory

-24.5MiB live, 24.4MiB allocated; 6ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

12.0ms	eps
8.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

23.7MiB live, 23.7MiB allocated; 0ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.9%	1	`x`
98.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

-27.1MiB live, 19.0MiB allocated; 2ms collecting garbage

Counts

24 → 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 (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))
#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 (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.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 (neg.f64 eps) #s(approx (sin x) (.f64 #s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 eps eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (neg.f64 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 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))))
#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 (neg.f64 eps) #s(approx (sin x) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) x (.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)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (.f64 (-.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) eps)) (.f64 x x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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)) (.f64 (neg.f64 eps) #s(approx (sin x) (.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 x x))) (.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) 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 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) x (.f64 #s(literal 1/6 binary64) eps)) eps) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps) #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 (* (* -2 (sin (/ (- x (- x eps)) 2))) (sin (/ (+ (+ eps x) x) 2))) (*.f64 #s(approx (* (sin (* 1/2 eps)) -2) (neg.f64 eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x 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
98.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.9%	1	`x`
98.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.2%)

Memory

18.3MiB live, 18.3MiB allocated; 0ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
96.6%	1	`x`
96.6%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

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

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.3%	1	`x`
96.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
96.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

-38.4MiB live, 8.1MiB allocated; 2ms 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 (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))
#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))))

Outputs
#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))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
78.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
78.9%	1	`x`
78.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms 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 (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (cos x) -1/2) (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/48 (* eps eps)) 1/4)) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 #s(approx (+ ( (+ (* (* eps eps) -1/48) 1/4) (* eps eps)) (neg (/ (+ (* (neg eps) (- (* (* eps eps) 1/6) 1)) (neg (* (* eps eps) (/ (- (* (* eps eps) 1/24) 1/2) x)))) x))) (/.f64 (neg.f64 eps) x)) (*.f64 x x)))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
78.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
78.6%	1	`x`
78.6%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

5.2MiB live, 5.2MiB 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
47.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
47.7%	1	`x`
47.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations354.0ms (4%)

Memory

9.5MiB live, 146.9MiB allocated; 12ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 537 to 143 computations (73.4% saved)

preprocess110.0ms (1.2%)

Memory: 18.7MiB live, 157.4MiB allocated; 42ms collecting garbage
Compiler: Compiled 1 148 to 348 computations (69.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze33.0ms (0.4%)

sample6.6s (74.1%)

explain185.0ms (2.1%)

preprocess98.0ms (1.1%)

series5.0ms (0.1%)

rewrite153.0ms (1.7%)

eval10.0ms (0.1%)

prune12.0ms (0.1%)

series44.0ms (0.5%)

rewrite226.0ms (2.5%)

eval61.0ms (0.7%)

prune24.0ms (0.3%)

series44.0ms (0.5%)

rewrite179.0ms (2%)

eval77.0ms (0.9%)

prune37.0ms (0.4%)

series46.0ms (0.5%)

rewrite234.0ms (2.6%)

eval61.0ms (0.7%)

prune45.0ms (0.5%)

regimes43.0ms (0.5%)

regimes33.0ms (0.4%)

regimes28.0ms (0.3%)

regimes30.0ms (0.3%)

regimes25.0ms (0.3%)

regimes28.0ms (0.3%)

regimes22.0ms (0.2%)

regimes21.0ms (0.2%)

regimes17.0ms (0.2%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

derivations354.0ms (4%)

preprocess110.0ms (1.2%)

end0.0ms (0%)

Profiling