Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

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

analyze27.0ms (0.3%)

Memory

37.3MiB live, 37.3MiB allocated; 0ms 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)

sample4.6s (56.5%)

Memory

118.5MiB live, 5 661.9MiB allocated; 2.0s collecting garbage

Samples

2.2s	26 581×	0	invalid
843.0ms	5 563×	1	valid
175.0ms	2 693×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-tan: 800.0ms (43.1% of total)

ival-fabs: 238.0ms (12.8% of total)

ival-add!: 217.0ms (11.7% of total)

adjust: 180.0ms (9.7% of total)

ival-<: 127.0ms (6.8% of total)

ival-mult!: 126.0ms (6.8% of total)

ival-sub!: 91.0ms (4.9% of total)

ival-and: 63.0ms (3.4% of total)

ival-assert: 13.0ms (0.7% of total)

Bogosity

preprocess45.0ms (0.6%)

Memory

-24.9MiB live, 67.8MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	84	42
2	388	42
3	2634	42

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 12 to 12 computations (0% saved)

series12.0ms (0.1%)

Memory

25.4MiB live, 25.4MiB allocated; 0ms collecting garbage

Counts

6 → 31

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos 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 (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))

rewrite194.0ms (2.4%)

Memory

24.1MiB live, 308.3MiB allocated; 44ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	1230
0	201	1087
1	1438	874
0	8690	844

Stop Event

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

Counts

37 → 119

Calls

Call 1

Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos 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 (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Outputs
(/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))))))
(/.f64 (-.f64 (.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (cos.f64 x))) (.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (cos.f64 x)) (.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (cos.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (sin.f64 x)))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))))
(/.f64 (neg.f64 (sin.f64 (-.f64 (+.f64 eps x) x))) (neg.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (tan.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(neg.f64 (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))
(fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
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x
eps
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(tan.f64 (+.f64 x (PI.f64)))
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#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
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#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
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eval14.0ms (0.2%)

Memory: -6.4MiB live, 41.0MiB allocated; 5ms collecting garbage
Compiler: Compiled 1 418 to 567 computations (60% saved)

prune12.0ms (0.1%)

Memory

-14.3MiB live, 32.0MiB allocated; 2ms collecting garbage

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	98	13	111
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	14	112

Accuracy

99.9%

Counts

112 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.2%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	61.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.4%	(-.f64 (+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
▶	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	60.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
▶	60.1%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	59.9%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (.f64 (.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
▶	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))

Compiler

Compiled 462 to 386 computations (16.5% saved)

series99.0ms (1.2%)

Memory

15.6MiB live, 255.4MiB allocated; 14ms collecting garbage

Counts

58 → 250

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 (-.f64 (neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (-.f64 (neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64))
(-.f64 (neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))))
(neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps))
(.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)
(+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64))
(+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))
#s(literal 1/2 binary64)
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))
eps
(neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(sin.f64 x)
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 eps)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)))
(+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))
(+.f64 (+.f64 eps x) (PI.f64))
(+.f64 eps x)
(PI.f64)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(+.f64 (tan.f64 x) (tan.f64 eps))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 x) (tan.f64 eps))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x))))))))
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#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* 4/3 (* eps (pow x 2))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* (pow x 2) (- (* 17/9 (* eps (pow x 2))) (* -4/3 eps))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* 248/135 (* eps (pow x 2))) (* -17/9 eps))) (* -4/3 eps))) (* -1/3 eps))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (* -1/3 eps)))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -4/3 (* eps (pow x 2))) (* -1/3 eps))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -1/3 eps) (* (pow x 2) (+ (* -17/9 (* eps (pow x 2))) (* -4/3 eps))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -1/3 eps) (* (pow x 2) (+ (* -4/3 eps) (* (pow x 2) (+ (* -17/9 eps) (* -248/135 (* eps (pow x 2))))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 -1/2))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#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) #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 (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow x 2)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (+ (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))) (/ (* x (pow (sin (+ eps (* 2 (PI)))) 2)) (pow (cos (+ eps (* 2 (PI)))) 2)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))) (cos (+ eps (* 2 (PI))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin (+ eps (* 2 (PI)))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (pow (cos (+ eps (* 2 (PI)))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (* 1/6 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))))) (* -1 (/ (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (cos (+ eps (* 2 (PI)))))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))) (cos (+ eps (* 2 (PI)))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ eps (* 2 (PI)))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (pow (cos (+ eps (* 2 (PI)))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (* 1/6 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))))) (* -1 (/ (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (cos (+ eps (* 2 (PI))))))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (+ eps (* 2 (PI)))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (+ eps (+ x (* 2 (PI))))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (+ eps (PI))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (+ eps (+ x (PI)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
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#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ x (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* x (- (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* x (- (* (pow x 2) (- (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (/ (* x (sin eps)) (cos eps))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
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#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (* -1 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* 2/15 (pow x 5))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* 2/15 (pow x 4))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* 2/15 (pow x 2))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* (pow x 2) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (- (/ (sin (+ eps (+ x (* 2 (PI))))) (cos (+ eps (+ x (* 2 (PI)))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (/ (sin (+ eps (+ x (* 2 (PI))))) (cos (+ eps (+ x (* 2 (PI))))))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (* x (+ 1 (+ (* 2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (* x (+ 1 (+ (/ eps x) (/ (PI) x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) #s(hole binary64 (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 2))) 2/15)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (- (/ (sin (- (+ eps (* 2 (PI))) (* -1 x))) (cos (- (+ eps (* 2 (PI))) (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (/ (sin (- (+ eps (* 2 (PI))) (* -1 x))) (cos (- (+ eps (* 2 (PI))) (* -1 x))))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 2 (PI))) x)) 1)))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (PI)) x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))
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Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) x 2 -1/2 (* (pow (tan x) 2) 1/6) 1/6 (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (- 1/2 (* 1/2 (cos (* 2 x)))) 1/2 (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))) eps (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (- 1 (neg (pow (tan x) 2))) (sin x)) (sin x) (cos x) (- (tan (+ x eps)) (tan x)) (tan eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) (+ (* 2/15 (* x x)) 1/3) 2/15 (* x x) 1/3 (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan (+ (+ (+ eps x) (PI)) (PI))) (+ (+ (+ eps x) (PI)) (PI)) (+ (+ eps x) (PI)) (+ eps x) (PI) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))) (* (tan x) (tan eps)))
18.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) x 2 -1/2 (* (pow (tan x) 2) 1/6) 1/6 (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (- 1/2 (* 1/2 (cos (* 2 x)))) 1/2 (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))) eps (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (- 1 (neg (pow (tan x) 2))) (sin x)) (sin x) (cos x) (- (tan (+ x eps)) (tan x)) (tan eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) (+ (* 2/15 (* x x)) 1/3) 2/15 (* x x) 1/3 (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan (+ (+ (+ eps x) (PI)) (PI))) (+ (+ (+ eps x) (PI)) (PI)) (+ (+ eps x) (PI)) (+ eps x) (PI) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))) (* (tan x) (tan eps)))
15.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) x 2 -1/2 (* (pow (tan x) 2) 1/6) 1/6 (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (- 1/2 (* 1/2 (cos (* 2 x)))) 1/2 (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))) eps (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (- 1 (neg (pow (tan x) 2))) (sin x)) (sin x) (cos x) (- (tan (+ x eps)) (tan x)) (tan eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) (+ (* 2/15 (* x x)) 1/3) 2/15 (* x x) 1/3 (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan (+ (+ (+ eps x) (PI)) (PI))) (+ (+ (+ eps x) (PI)) (PI)) (+ (+ eps x) (PI)) (+ eps x) (PI) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))) (* (tan x) (tan eps)))
15.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) x 2 -1/2 (* (pow (tan x) 2) 1/6) 1/6 (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (- 1/2 (* 1/2 (cos (* 2 x)))) 1/2 (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))) eps (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (- 1 (neg (pow (tan x) 2))) (sin x)) (sin x) (cos x) (- (tan (+ x eps)) (tan x)) (tan eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) (+ (* 2/15 (* x x)) 1/3) 2/15 (* x x) 1/3 (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan (+ (+ (+ eps x) (PI)) (PI))) (+ (+ (+ eps x) (PI)) (PI)) (+ (+ eps x) (PI)) (+ eps x) (PI) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))) (* (tan x) (tan eps)))
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rewrite551.0ms (6.8%)

Memory

-53.8MiB live, 386.9MiB allocated; 706ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1311	14069
0	1413	11894
0	8219	11668

Stop Event

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

Counts

308 → 470

Calls

Call 1

Inputs
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eps
(neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(sin.f64 x)
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 eps)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)))
(+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))
(+.f64 (+.f64 eps x) (PI.f64))
(+.f64 eps x)
(PI.f64)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(+.f64 (tan.f64 x) (tan.f64 eps))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 x) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* 4/3 (* eps (pow x 2))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* (pow x 2) (- (* 17/9 (* eps (pow x 2))) (* -4/3 eps))) (* -1/3 eps))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* 248/135 (* eps (pow x 2))) (* -17/9 eps))) (* -4/3 eps))) (* -1/3 eps))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (* -1/3 eps)))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -4/3 (* eps (pow x 2))) (* -1/3 eps))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -1/3 eps) (* (pow x 2) (+ (* -17/9 (* eps (pow x 2))) (* -4/3 eps))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (+ (* -1/3 eps) (* (pow x 2) (+ (* -4/3 eps) (* (pow x 2) (+ (* -17/9 eps) (* -248/135 (* eps (pow x 2))))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 -1/2))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#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) #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 (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow x 2)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI)))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (+ (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))) (/ (* x (pow (sin (+ eps (* 2 (PI)))) 2)) (pow (cos (+ eps (* 2 (PI)))) 2)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))) (cos (+ eps (* 2 (PI))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin (+ eps (* 2 (PI)))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (pow (cos (+ eps (* 2 (PI)))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (* 1/6 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))))) (* -1 (/ (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (cos (+ eps (* 2 (PI)))))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))) (cos (+ eps (* 2 (PI)))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ eps (* 2 (PI)))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (pow (cos (+ eps (* 2 (PI)))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (* 1/6 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2)))))))) (* -1 (/ (* (sin (+ eps (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (cos (+ eps (* 2 (PI))))))))) (* -1 (/ (pow (sin (+ eps (* 2 (PI)))) 2) (pow (cos (+ eps (* 2 (PI)))) 2))))) (/ (sin (+ eps (* 2 (PI)))) (cos (+ eps (* 2 (PI))))))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (+ eps (* 2 (PI)))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (+ eps (+ x (* 2 (PI))))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (+ eps (PI))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (+ eps (+ x (PI)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ x (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* x (- (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* x (- (* (pow x 2) (- (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (/ (* x (sin eps)) (cos eps))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) #s(hole binary64 (* -1 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) #s(hole binary64 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) #s(hole binary64 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* 2/15 (pow x 5))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* 2/15 (pow x 4))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 2/15 (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* 2/15 (pow x 2))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (* (pow x 2) (+ 2/15 (* 1/3 (/ 1 (pow x 2)))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (- (/ (sin (+ eps (+ x (* 2 (PI))))) (cos (+ eps (+ x (* 2 (PI)))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (/ (sin (+ eps (+ x (* 2 (PI))))) (cos (+ eps (+ x (* 2 (PI))))))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (* x (+ 1 (+ (* 2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (* x (+ 1 (+ (/ eps x) (/ (PI) x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) #s(hole binary64 (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 2))) 2/15)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (- (/ (sin (- (+ eps (* 2 (PI))) (* -1 x))) (cos (- (+ eps (* 2 (PI))) (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (/ (sin (- (+ eps (* 2 (PI))) (* -1 x))) (cos (- (+ eps (* 2 (PI))) (* -1 x))))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 2 (PI))) x)) 1)))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (PI)) x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* eps (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (* eps (+ 1 (+ (* 2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (* eps (+ 1 (+ (/ x eps) (/ (PI) eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* (pow eps 2) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))))))
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#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) #s(hole binary64 (- (/ (sin (- (+ x (* 2 (PI))) (* -1 eps))) (cos (- (+ x (* 2 (PI))) (* -1 eps)))) (/ (sin x) (cos x)))))
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#s(approx (+ (+ (+ eps x) (PI)) (PI)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 2 (PI))) eps)) 1)))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (PI)) eps)) 1)))))

Outputs
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(.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (-.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) #s(literal -1/6 binary64)) (neg.f64 eps) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps)
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(*.f64 (pow.f64 (sin.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 1 binary64)))
(*.f64 (sin.f64 x) (sin.f64 x))
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(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 2 binary64)))
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#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))
(sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
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(cos.f64 (neg.f64 (+.f64 x x)))
(cos.f64 (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 x x)
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(*.f64 (cos.f64 x) (cos.f64 x))
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(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))
(-.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)))
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eps
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(sin.f64 x)
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(cos.f64 x)
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(*.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
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(tan.f64 (+.f64 (+.f64 x eps) (PI.f64)))
(tan.f64 (+.f64 x eps))
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(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))
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(neg.f64 (-.f64 (neg.f64 eps) x))
(-.f64 x (neg.f64 eps))
(+.f64 x (*.f64 #s(literal 1 binary64) eps))
(+.f64 x (neg.f64 (neg.f64 eps)))
(+.f64 x eps)
#s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x)) (.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x))) #s(literal 1 binary64)) (-.f64 (.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x)) #s(literal 1 binary64)))
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(fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))
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(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(-.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(+.f64 (.f64 #s(literal 2/15 binary64) (.f64 x x)) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(literal 1/3 binary64)
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(-.f64 (+.f64 eps x) (neg.f64 (PI.f64)))
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(PI.f64)
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#s(approx (* (pow (tan x) 2) 1/6) (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/9 binary64) (.f64 x x)))))
#s(approx (* (pow (tan x) 2) 1/6) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -17/270 binary64) (.f64 x x)))))))
#s(approx (* (pow (tan x) 2) 1/6) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 17/270 binary64) (.f64 #s(literal -31/945 binary64) (.f64 x x)))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (.f64 (.f64 x x) (fma.f64 #s(literal -5/3 binary64) (*.f64 x x) #s(literal -1 binary64))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -77/45 binary64) (.f64 x x) #s(literal -5/3 binary64)) #s(literal -1 binary64))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -88/63 binary64) (*.f64 x x) #s(literal -77/45 binary64)) #s(literal -5/3 binary64)) #s(literal -1 binary64))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -5/3 binary64) (.f64 x x)))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 5/3 binary64) (.f64 #s(literal -77/45 binary64) (.f64 x x)))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/3 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 77/45 binary64) (.f64 #s(literal -88/63 binary64) (.f64 x x)))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 #s(literal 2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (-.f64 #s(literal 2/45 binary64) (.f64 #s(literal 1/315 binary64) (*.f64 x x))) #s(literal -1/3 binary64))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (cos (* 2 x))) (+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 x x))))
#s(approx (* 1/2 (cos (* 2 x))) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))))
#s(approx (* 1/2 (cos (* 2 x))) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/45 binary64) (*.f64 x x))) #s(literal -1 binary64)))))
#s(approx (cos (* 2 x)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 x x))))
#s(approx (cos (* 2 x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal -2 binary64)))))
#s(approx (cos (* 2 x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (-.f64 #s(literal 2/3 binary64) (.f64 #s(literal 4/45 binary64) (*.f64 x x))) #s(literal -2 binary64)))))
#s(approx (* 2 x) (+.f64 x x))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2 binary64) (.f64 x x))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 2 binary64) (.f64 #s(literal -7/3 binary64) (.f64 x x))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 7/3 binary64) (.f64 #s(literal -94/45 binary64) (.f64 x x))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/45 binary64) (*.f64 x x))) #s(literal -1 binary64)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (neg.f64 x))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (.f64 x (fma.f64 #s(literal -4/3 binary64) (.f64 x x) #s(literal -1 binary64))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -17/15 binary64) (*.f64 x x) #s(literal -4/3 binary64)) #s(literal -1 binary64))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -248/315 binary64) (.f64 x x) #s(literal -17/15 binary64)) #s(literal -4/3 binary64)) #s(literal -1 binary64))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 x x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 4/3 binary64) (.f64 #s(literal -17/15 binary64) (*.f64 x x)))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 17/15 binary64) (.f64 #s(literal -248/315 binary64) (*.f64 x x)))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -5/6 binary64) (*.f64 x x)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 5/6 binary64) (.f64 #s(literal -61/120 binary64) (*.f64 x x)))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/6 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 61/120 binary64) (.f64 #s(literal -277/1008 binary64) (*.f64 x x)))))))))
#s(approx (sin x) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
#s(approx (sin x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64))))))
#s(approx (sin x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (-.f64 #s(literal 1/120 binary64) (.f64 #s(literal 1/5040 binary64) (.f64 x x))) #s(literal -1/6 binary64))))))
#s(approx (cos x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/720 binary64) (*.f64 x x))) #s(literal -1/2 binary64)))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (fma.f64 x (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (fma.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 (sin.f64 eps) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))) (cos.f64 eps))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (fma.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (+.f64 (neg.f64 (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))))) (neg.f64 (/.f64 (*.f64 (sin.f64 eps) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (cos.f64 eps)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 x x))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 x x))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(literal 1/3 binary64))
#s(approx (+ (* 2/15 (* x x)) 1/3) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 x x))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (+.f64 (tan.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) (/.f64 (*.f64 x (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (fma.f64 x (-.f64 (/.f64 (.f64 x (.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))))) (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (tan.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (fma.f64 x (-.f64 (.f64 x (-.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (+.f64 (neg.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))))) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))))))) (neg.f64 (/.f64 (*.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))))) (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (tan.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) (fma.f64 x (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (tan.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) (fma.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))))) (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (tan.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64))))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) (fma.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (+.f64 (neg.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))))) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))))))) (neg.f64 (/.f64 (*.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)))))) (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64))))))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64)) (pow.f64 (cos.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64)))) #s(literal 2 binary64))))) (tan.f64 (+.f64 eps (+.f64 (PI.f64) (PI.f64))))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) (+.f64 eps (+.f64 (PI.f64) (PI.f64))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) (+.f64 eps (+.f64 x (+.f64 (PI.f64) (PI.f64)))))
#s(approx (+ (+ eps x) (PI)) (+.f64 eps (PI.f64)))
#s(approx (+ (+ eps x) (PI)) (+.f64 eps (+.f64 x (PI.f64))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (fma.f64 x (-.f64 (neg.f64 (*.f64 x (+.f64 (neg.f64 (tan.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (fma.f64 x (-.f64 (.f64 x (-.f64 (neg.f64 (.f64 x (+.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (-.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 4 binary64)))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))) (+.f64 (neg.f64 (tan.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
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#s(approx (+ (tan x) (tan eps)) (+.f64 x (tan.f64 eps)))
#s(approx (+ (tan x) (tan eps)) (fma.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 x x))) (tan.f64 eps)))
#s(approx (+ (tan x) (tan eps)) (fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 x x))))) (tan.f64 eps)))
#s(approx (- 1 (* (tan x) (tan eps))) (+.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (*.f64 x (sin.f64 eps)) (cos.f64 eps)))))
#s(approx (- 1 (* (tan x) (tan eps))) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal -1/3 binary64) (/.f64 (.f64 (.f64 x x) (sin.f64 eps)) (cos.f64 eps))) (tan.f64 eps)))))
#s(approx (- 1 (* (tan x) (tan eps))) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal -2/15 binary64) (/.f64 (.f64 (.f64 x x) (sin.f64 eps)) (cos.f64 eps)) (.f64 #s(literal -1/3 binary64) (tan.f64 eps)))) (tan.f64 eps)))))
#s(approx (* (tan x) (tan eps)) (/.f64 (*.f64 x (sin.f64 eps)) (cos.f64 eps)))
#s(approx (* (tan x) (tan eps)) (.f64 x (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 (*.f64 x x) (sin.f64 eps)) (cos.f64 eps)) (tan.f64 eps))))
#s(approx (* (tan x) (tan eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 2/15 binary64) (/.f64 (.f64 (.f64 x x) (sin.f64 eps)) (cos.f64 eps)) (*.f64 #s(literal 1/3 binary64) (tan.f64 eps))) (tan.f64 eps))))
#s(approx (* (tan x) (tan eps)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (tan.f64 eps) (.f64 (.f64 x x) (fma.f64 #s(literal 17/315 binary64) (/.f64 (.f64 (.f64 x x) (sin.f64 eps)) (cos.f64 eps)) (*.f64 #s(literal 2/15 binary64) (tan.f64 eps))))) (tan.f64 eps))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x)) (.f64 eps (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x)) (.f64 eps (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (+.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x)) (.f64 eps (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x)) (.f64 eps (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))))
#s(approx (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg.f64 (.f64 eps (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))))
#s(approx (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps) (.f64 eps (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))
#s(approx (- 1 (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))
#s(approx (neg (pow (tan x) 2)) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))
#s(approx (pow (tan x) 2) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
#s(approx (tan x) (tan.f64 x))
#s(approx (* (pow (tan x) 2) 1/6) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (neg.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
#s(approx (* 1/2 (cos (* 2 x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
#s(approx (cos (* 2 x)) (cos.f64 (+.f64 x x)))
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#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan.f64 (+.f64 x eps)))
#s(approx (+ x eps) (neg.f64 (*.f64 eps (-.f64 (neg.f64 (/.f64 x eps)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (-.f64 (tan.f64 (-.f64 (+.f64 x (+.f64 (PI.f64) (PI.f64))) (neg.f64 eps))) (tan.f64 x)))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) (tan.f64 (-.f64 (+.f64 x (+.f64 (PI.f64) (PI.f64))) (neg.f64 eps))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) (neg.f64 (*.f64 eps (-.f64 (neg.f64 (/.f64 (+.f64 x (+.f64 (PI.f64) (PI.f64))) eps)) #s(literal 1 binary64)))))
#s(approx (+ (+ eps x) (PI)) (neg.f64 (*.f64 eps (-.f64 (neg.f64 (/.f64 (+.f64 x (PI.f64)) eps)) #s(literal 1 binary64)))))

eval166.0ms (2%)

Memory: -34.9MiB live, 114.7MiB allocated; 101ms collecting garbage
Compiler: Compiled 15 086 to 3 961 computations (73.7% saved)

prune30.0ms (0.4%)

Memory

2.4MiB live, 48.5MiB allocated; 5ms collecting garbage

Pruning

27 alts after pruning (22 fresh and 5 done)

	Pruned	Kept	Total
New	430	17	447
Fresh	3	5	8
Picked	1	4	5
Done	0	1	1
Total	434	27	461

Accuracy

99.9%

Counts

461 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.5%	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
▶	61.2%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	61.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.3%	(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
	61.2%	(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	60.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
✓	60.1%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)))) (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 x (*.f64 #s(literal -1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
▶	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
	47.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (.f64 (.f64 eps eps) (+.f64 (-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) eps))) eps))))) eps))
	4.2%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
✓	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
	33.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (.f64 (.f64 (.f64 eps eps) eps) (-.f64 (+.f64 #s(literal 1/6 binary64) (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 eps (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) eps)) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))

Compiler

Compiled 2 178 to 1 563 computations (28.2% saved)

series75.0ms (0.9%)

Memory

21.2MiB live, 73.8MiB allocated; 27ms collecting garbage

Counts

47 → 190

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* 5/6 eps) (* -1/2 eps))))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (* 5/6 eps) (* -1/2 eps))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (+ (* 5/6 eps) (* (pow x 2) (- (* 61/120 eps) (+ (* -1/2 (- (* 5/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#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) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (- 1 (* -4/3 (pow eps 2))))))))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (* 1/3 (pow eps 2))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* eps x))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (- 1 (* -4/3 (pow eps 2)))))))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* eps x)))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* x (+ eps (* x (- 1 (* -4/3 (pow eps 2))))))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (+ eps (* x (- 1 (* -4/3 (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* x (- 1 (* -4/3 (pow eps 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 4/3 (* (pow eps 2) x))))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
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#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* 4/3 (* (pow eps 2) (pow x 2)))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 (pow x 2)) (/ x eps)))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* 4/3 (* (pow eps 2) x))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 x) (/ 1 eps)))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 x) (/ x (pow eps 2))))))
#s(approx (- 1 (* -4/3 (* eps eps))) #s(hole binary64 (* 4/3 (pow eps 2))))
#s(approx (- 1 (* -4/3 (* eps eps))) #s(hole binary64 (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
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#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
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Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (- 1 (neg (pow (tan x) 2))) (sin x)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) x 2 (sin x) (cos x) (- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (- 1 (* -1/3 (* eps eps))) (* -1/3 (* eps eps)) -1/3 (* eps eps) (- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) 1/3 (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) (+ eps (* x (- 1 (* -4/3 (* eps eps))))) (* x (- 1 (* -4/3 (* eps eps)))) (- 1 (* -4/3 (* eps eps))) (* -4/3 (* eps eps)) -4/3 (- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (* 1/3 eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)))
8.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (- 1 (neg (pow (tan x) 2))) (sin x)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) x 2 (sin x) (cos x) (- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (- 1 (* -1/3 (* eps eps))) (* -1/3 (* eps eps)) -1/3 (* eps eps) (- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) 1/3 (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) (+ eps (* x (- 1 (* -4/3 (* eps eps))))) (* x (- 1 (* -4/3 (* eps eps)))) (- 1 (* -4/3 (* eps eps))) (* -4/3 (* eps eps)) -4/3 (- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (* 1/3 eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)))
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rewrite300.0ms (3.7%)

Memory

0.5MiB live, 229.6MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	983	11030
0	1042	9451
1	7110	9451
0	8409	8869

Stop Event

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

Counts

237 → 431

Calls

Call 1

Inputs
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#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- x (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1/3 eps))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 4/3 x) (* -4/3 eps))))) (* -1/3 eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow x 2) (- 1 (* -4/3 (pow eps 2))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow x 2) (- (+ 1 (/ eps x)) (* -4/3 (pow eps 2))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow x 2) (- (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (/ 1 (pow x 2)) (/ eps x)))) (* -4/3 (pow eps 2))))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (* (pow x 2) (- (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (/ eps x))) (* -4/3 (pow eps 2))))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* x (- (+ 1 (/ eps x)) (* -4/3 (pow eps 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (- (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow x 2) (- (+ 1 (* -1 (/ (+ (* -1 eps) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x))) (* -4/3 (pow eps 2))))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (* (pow x 2) (- (+ 1 (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x))) (* -4/3 (pow eps 2))))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* -1 (* x (+ (* -1 (- 1 (* -4/3 (pow eps 2)))) (* -1 (/ eps x)))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* -1/3 (* eps eps)) #s(hole binary64 (* -1/3 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (+ 1 (+ (* eps x) (pow x 2)))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2)))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (+ (* eps x) (pow x 2))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (+ x (* eps (+ 1 (* 4/3 (* eps x)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (+ x (* 4/3 (* (pow eps 2) x)))))
#s(approx (- 1 (* -4/3 (* eps eps))) #s(hole binary64 (+ 1 (* 4/3 (pow eps 2)))))
#s(approx (* -4/3 (* eps eps)) #s(hole binary64 (* -4/3 (pow eps 2))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (/ (* (pow eps 2) (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* (pow eps 2) (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* eps (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* eps (+ (/ 1 eps) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* (pow eps 3) (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* (pow eps 3) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
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#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (- 1 (* -1/3 (* eps eps))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* 4/3 (* (pow eps 2) (pow x 2)))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 (pow x 2)) (/ x eps)))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* 4/3 (* (pow eps 2) x))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 x) (/ 1 eps)))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* (pow eps 2) (+ (* 4/3 x) (/ x (pow eps 2))))))
#s(approx (- 1 (* -4/3 (* eps eps))) #s(hole binary64 (* 4/3 (pow eps 2))))
#s(approx (- 1 (* -4/3 (* eps eps))) #s(hole binary64 (* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* eps (- (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* eps (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ 1/6 (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* (pow eps 2) (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
#s(approx (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps))))))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))))
#s(approx (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2))))))
#s(approx (+ eps (* x (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)))))
#s(approx (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* -1 (/ (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps)) eps))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* -1 (* eps (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))
#s(approx (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (- (+ 1/6 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))

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

eval68.0ms (0.8%)

Memory: -24.3MiB live, 118.2MiB allocated; 21ms collecting garbage
Compiler: Compiled 10 922 to 2 784 computations (74.5% saved)

prune36.0ms (0.4%)

Memory

28.7MiB live, 74.5MiB allocated; 4ms collecting garbage

Pruning

39 alts after pruning (34 fresh and 5 done)

	Pruned	Kept	Total
New	409	26	435
Fresh	9	8	17
Picked	5	0	5
Done	0	5	5
Total	423	39	462

Accuracy

99.9%

Counts

462 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.5%	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
▶	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.7%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.6%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	61.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.3%	(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
	61.2%	(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	60.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
✓	60.1%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
	99.1%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) eps))
	96.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
▶	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
	6.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
	4.2%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
✓	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
	33.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (.f64 (.f64 (.f64 eps eps) eps) (-.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (neg.f64 (/.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) (/.f64 #s(literal 1 binary64) eps)) eps))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))) (.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))))))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
▶	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
▶	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))

Compiler

Compiled 2 902 to 2 267 computations (21.9% saved)

series53.0ms (0.7%)

Memory

-19.3MiB live, 72.8MiB allocated; 6ms collecting garbage

Counts

49 → 167

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64))
(fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
(*.f64 eps eps)
eps
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps))))
(-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))
#s(literal 1/3 binary64)
(.f64 #s(literal -2/15 binary64) (.f64 eps eps))
#s(literal -2/15 binary64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (+.f64 x x))
(+.f64 x x)
#s(literal 1/2 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 17/15 binary64) (*.f64 x x) #s(literal 4/3 binary64))
#s(literal 17/15 binary64)
(*.f64 x x)
#s(literal 4/3 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
#s(literal 2 binary64)

Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #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 (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (+ x x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (+ x x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (+ x x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* 5/6 eps) (* -1/2 eps))))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (* 5/6 eps) (* -1/2 eps))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (+ (* 5/6 eps) (* (pow x 2) (- (* 61/120 eps) (+ (* -1/2 (- (* 5/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 4/3 (pow x 2)))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2)))))))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 4/3))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 (+ 4/3 (* 17/15 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (cos (+ x x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* 17/15 (pow x 5))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/15 (* 4/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/15 (+ (* 4/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (* 17/15 (pow x 4))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 17/15 (* 4/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 17/15 (+ (* 4/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 (* 17/15 (pow x 2))))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 (* (pow x 2) (+ 17/15 (* 4/3 (/ 1 (pow x 2)))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))
#s(approx (cos (+ x x)) #s(hole binary64 (cos (neg (* -2 x)))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 4/3 (/ 1 (pow x 2))) (pow x 2))) 17/15)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 -1/6))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (- (* 1/120 (pow eps 2)) 1/6)))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow eps 2)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))))
#s(approx (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) #s(hole binary64 (* 1/3 (pow eps 2))))
#s(approx (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 1/3))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 (+ 1/3 (* 2/15 (pow eps 2)))))
#s(approx (* -2/15 (* eps eps)) #s(hole binary64 (* -2/15 (pow eps 2))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1/5040 (pow eps 7))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 7) (- (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* -1/5040 (pow eps 6))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* (pow eps 6) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* (pow eps 6) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* (pow eps 6) (- (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (* -1/5040 (pow eps 4))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 (* -1/5040 (pow eps 2))))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 (* (pow eps 2) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (/ (* (pow eps 2) (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* (pow eps 2) (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* 2/15 (pow eps 5))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* (pow eps 5) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* (pow eps 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow eps 2))) (/ 1 (pow eps 4)))))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (* 2/15 (pow eps 4))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/15 (+ (* 1/3 (/ 1 (pow eps 2))) (/ 1 (pow eps 4)))))))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 (* 2/15 (pow eps 2))))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 (* (pow eps 2) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* eps (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* eps (+ (/ 1 eps) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- 1/5040 (* 1/120 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (* 1/120 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* -1 (* (pow eps 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow eps 2))) (pow eps 2))) 2/15)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps))))))

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	eps	@	0	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (+ (* -1/5040 (* eps eps)) 1/120) -1/5040 (* eps eps) eps 1/120 -1/6 1 (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) (- 1/3 (* -2/15 (* eps eps))) 1/3 (* -2/15 (* eps eps)) -2/15 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (+ (* (cos (+ x x)) 1/2) 1/2) (cos (+ x x)) (+ x x) 1/2 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (+ (* 17/15 (* x x)) 4/3) 17/15 (* x x) 4/3 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) 2)
10.0ms	eps	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (+ (* -1/5040 (* eps eps)) 1/120) -1/5040 (* eps eps) eps 1/120 -1/6 1 (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) (- 1/3 (* -2/15 (* eps eps))) 1/3 (* -2/15 (* eps eps)) -2/15 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (+ (* (cos (+ x x)) 1/2) 1/2) (cos (+ x x)) (+ x x) 1/2 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (+ (* 17/15 (* x x)) 4/3) 17/15 (* x x) 4/3 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) 2)
7.0ms	x	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (+ (* -1/5040 (* eps eps)) 1/120) -1/5040 (* eps eps) eps 1/120 -1/6 1 (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) (- 1/3 (* -2/15 (* eps eps))) 1/3 (* -2/15 (* eps eps)) -2/15 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (+ (* (cos (+ x x)) 1/2) 1/2) (cos (+ x x)) (+ x x) 1/2 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (+ (* 17/15 (* x x)) 4/3) 17/15 (* x x) 4/3 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) 2)
6.0ms	eps	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (+ (* -1/5040 (* eps eps)) 1/120) -1/5040 (* eps eps) eps 1/120 -1/6 1 (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) (- 1/3 (* -2/15 (* eps eps))) 1/3 (* -2/15 (* eps eps)) -2/15 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (+ (* (cos (+ x x)) 1/2) 1/2) (cos (+ x x)) (+ x x) 1/2 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (+ (* 17/15 (* x x)) 4/3) 17/15 (* x x) 4/3 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) 2)
5.0ms	x	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (+ (* -1/5040 (* eps eps)) 1/120) -1/5040 (* eps eps) eps 1/120 -1/6 1 (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) (- 1/3 (* -2/15 (* eps eps))) 1/3 (* -2/15 (* eps eps)) -2/15 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (+ (* (cos (+ x x)) 1/2) 1/2) (cos (+ x x)) (+ x x) 1/2 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (+ (* 17/15 (* x x)) 4/3) 17/15 (* x x) 4/3 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) 2)

rewrite239.0ms (2.9%)

Memory

6.0MiB live, 250.4MiB allocated; 90ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	825	5286
0	883	4672
1	5523	4668
0	8153	4432

Stop Event

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

Counts

216 → 481

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64))
(fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
(*.f64 eps eps)
eps
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))))
(.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps))))
(-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))
#s(literal 1/3 binary64)
(.f64 #s(literal -2/15 binary64) (.f64 eps eps))
#s(literal -2/15 binary64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (+.f64 x x))
(+.f64 x x)
#s(literal 1/2 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 17/15 binary64) (*.f64 x x) #s(literal 4/3 binary64))
#s(literal 17/15 binary64)
(*.f64 x x)
#s(literal 4/3 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
#s(literal 2 binary64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #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 (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (+ x x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (+ x x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (+ x x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* 5/6 eps) (* -1/2 eps))))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (* 5/6 eps) (* -1/2 eps))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (+ (* 5/6 eps) (* (pow x 2) (- (* 61/120 eps) (+ (* -1/2 (- (* 5/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 4/3 (pow x 2)))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2)))))))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 4/3))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 (+ 4/3 (* 17/15 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (cos (+ x x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* 17/15 (pow x 5))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/15 (* 4/3 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 17/15 (+ (* 4/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (* 17/15 (pow x 4))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 17/15 (* 4/3 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 17/15 (+ (* 4/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 (* 17/15 (pow x 2))))
#s(approx (+ (* 17/15 (* x x)) 4/3) #s(hole binary64 (* (pow x 2) (+ 17/15 (* 4/3 (/ 1 (pow x 2)))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) #s(hole binary64 (/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) #s(hole binary64 (+ 1/2 (* 1/2 (cos (neg (* -2 x)))))))
#s(approx (cos (+ x x)) #s(hole binary64 (cos (neg (* -2 x)))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 4/3 (/ 1 (pow x 2))) (pow x 2))) 17/15)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 -1/6))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (- (* 1/120 (pow eps 2)) 1/6)))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow eps 2)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))))
#s(approx (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) #s(hole binary64 (* 1/3 (pow eps 2))))
#s(approx (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 1/3))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 (+ 1/3 (* 2/15 (pow eps 2)))))
#s(approx (* -2/15 (* eps eps)) #s(hole binary64 (* -2/15 (pow eps 2))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1/5040 (pow eps 7))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 7) (- (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* -1/5040 (pow eps 6))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* (pow eps 6) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* (pow eps 6) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) #s(hole binary64 (* (pow eps 6) (- (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (* -1/5040 (pow eps 4))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(hole binary64 (* (pow eps 4) (- (* 1/120 (/ 1 (pow eps 2))) (+ 1/5040 (/ 1/6 (pow eps 4)))))))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 (* -1/5040 (pow eps 2))))
#s(approx (+ (* -1/5040 (* eps eps)) 1/120) #s(hole binary64 (* (pow eps 2) (- (* 1/120 (/ 1 (pow eps 2))) 1/5040))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (/ (* (pow eps 2) (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* (pow eps 2) (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* 2/15 (pow eps 5))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* (pow eps 5) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* (pow eps 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow eps 2))) (/ 1 (pow eps 4)))))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (* 2/15 (pow eps 4))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/15 (+ (* 1/3 (/ 1 (pow eps 2))) (/ 1 (pow eps 4)))))))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 (* 2/15 (pow eps 2))))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(hole binary64 (* (pow eps 2) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* eps (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* eps (+ (/ 1 eps) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- 1/5040 (* 1/120 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (* 1/120 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/5040 (/ 1/6 (pow eps 4))) (+ (* 1/120 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) #s(hole binary64 (* -1 (* (pow eps 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow eps 2))) (pow eps 2))) 2/15)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps))))))

Outputs
(.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps))) (neg.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (neg.f64 eps) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) eps))
(fma.f64 #s(literal 1 binary64) eps (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) eps))
(fma.f64 eps #s(literal 1 binary64) (.f64 eps (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps)))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 eps (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps)))
(+.f64 (neg.f64 (neg.f64 eps)) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) eps))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 1 binary64)))))
(fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(-.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64))))
(-.f64 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps)))
(+.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal -1/6 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal 1/6 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 3 binary64)) #s(literal -1/216 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal -1/6 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 3 binary64)) #s(literal 1/216 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 2 binary64)) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)))))
(neg.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps)))
(fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps #s(literal -1/6 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(-.f64 (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64))
(+.f64 (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps) #s(literal -1/6 binary64))
(+.f64 #s(literal -1/6 binary64) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) eps) eps))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) (.f64 (.f64 eps eps) #s(literal -1/5040 binary64))) #s(literal 1/14400 binary64)) (-.f64 (.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))
(/.f64 (-.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)))) (-.f64 #s(literal 1/120 binary64) (.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))))
(/.f64 (fma.f64 #s(literal -1/128024064000 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)) #s(literal 1/1728000 binary64)) (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) (-.f64 #s(literal 1/14400 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)))))
(/.f64 (+.f64 #s(literal 1/1728000 binary64) (.f64 #s(literal -1/128024064000 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)))) (+.f64 #s(literal 1/14400 binary64) (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) (.f64 (.f64 eps eps) #s(literal -1/5040 binary64))) (.f64 #s(literal 1/120 binary64) (.f64 (.f64 eps eps) #s(literal -1/5040 binary64))))))
(fma.f64 (*.f64 #s(literal -1/5040 binary64) eps) eps #s(literal 1/120 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64))
(-.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))
(-.f64 #s(literal 1/120 binary64) (.f64 #s(literal 1/5040 binary64) (.f64 eps eps)))
(-.f64 #s(literal 1/120 binary64) (neg.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64))))
(+.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))
(+.f64 #s(literal 1/120 binary64) (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)))
#s(literal -1/5040 binary64)
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) eps)
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 eps) #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))
eps
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) x)) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (-.f64 x (+.f64 x eps))) (cos.f64 (-.f64 (+.f64 x eps) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (+.f64 x eps))) (cos.f64 (-.f64 (neg.f64 x) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 x (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (+.f64 x eps) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps)))) (sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps))) (sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 x eps))) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 2 binary64))
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#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps #s(literal 4/3 binary64)) x) eps eps) x (*.f64 eps eps)) x eps))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (.f64 eps #s(literal -2/3 binary64))) (neg.f64 eps)) (.f64 x x) eps))
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#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))
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#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
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#s(approx (cos (+ x x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -4/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal -2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ x x) (+.f64 x x))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64)))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64)))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (fma.f64 (fma.f64 (.f64 eps #s(literal 4/3 binary64)) (.f64 x x) eps) x #s(literal 1 binary64)))
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#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 248/315 binary64) (.f64 x x) #s(literal 17/15 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
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#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)))
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#s(approx (+ (* 17/15 (* x x)) 4/3) (fma.f64 (*.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)))
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#s(approx (neg (pow (tan x) 2)) (neg.f64 (*.f64 x x)))
#s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))
#s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))
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#s(approx (pow (tan x) 2) (.f64 (fma.f64 #s(literal 2/3 binary64) (.f64 x x) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
#s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 x eps)))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (cos x) (cos.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (.f64 (+.f64 (fma.f64 eps (.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) eps))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (cos (+ x x)) (cos.f64 (+.f64 x x)))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 eps (.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (fma.f64 eps (.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) #s(literal 1 binary64)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 17/15 binary64)))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 4/3 binary64) (.f64 x x)) #s(literal 17/15 binary64))))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 4/3 binary64)) (*.f64 x x)) #s(literal 17/15 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/15 binary64)))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 x x)) #s(literal 17/15 binary64))))
#s(approx (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) (.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 4/3 binary64)) (.f64 x x)) #s(literal 17/15 binary64)) (.f64 (.f64 x x) (.f64 x x))))
#s(approx (+ (* 17/15 (* x x)) 4/3) (.f64 (.f64 x x) #s(literal 17/15 binary64)))
#s(approx (+ (* 17/15 (* x x)) 4/3) (.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (.f64 x x)) #s(literal 17/15 binary64)) (*.f64 x x)))
#s(approx (neg (pow (tan x) 2)) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (pow (tan x) 2) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (tan x) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 x eps)))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
#s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (cos (+ x x)) (cos.f64 (+.f64 x x)))
#s(approx (* (+ (* (+ (* 17/15 (* x x)) 4/3) (* x x)) 1) x) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 4/3 binary64)) (*.f64 x x))) #s(literal 17/15 binary64)) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (cos.f64 x) #s(literal -4 binary64))))) (/.f64 #s(literal 1/6 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) eps) (neg.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -3 binary64))))) eps (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (neg.f64 eps) (fma.f64 (.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (cos.f64 x) #s(literal -4 binary64))))) (/.f64 #s(literal 1/6 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 x)) (cos.f64 x)))) (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (cos.f64 x) #s(literal -4 binary64))))) (/.f64 #s(literal 1/6 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) eps) (neg.f64 (*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -3 binary64))))) eps (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) eps))
#s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) #s(literal -1/6 binary64))
#s(approx (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
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#s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
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#s(approx (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps))))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))
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#s(approx (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))) (.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps)))
#s(approx (- 1/3 (* -2/15 (* eps eps))) #s(literal 1/3 binary64))
#s(approx (- 1/3 (* -2/15 (* eps eps))) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)))
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#s(approx (+ (* (+ (* (+ (* -1/5040 (* eps eps)) 1/120) (* eps eps)) -1/6) (* eps eps)) 1) (.f64 (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) #s(literal 1/5040 binary64))))
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#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 x eps)))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
#s(approx (* eps (+ 1 (* (* eps eps) (- 1/3 (* -2/15 (* eps eps)))))) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/3 binary64)) (*.f64 eps eps))) #s(literal 2/15 binary64)) (pow.f64 eps #s(literal 5 binary64)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) eps)) (neg.f64 (.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)))))

eval94.0ms (1.2%)

Memory: 30.4MiB live, 75.3MiB allocated; 4ms collecting garbage
Compiler: Compiled 6 622 to 2 782 computations (58% saved)

prune65.0ms (0.8%)

Memory

8.1MiB live, 99.3MiB allocated; 7ms collecting garbage

Pruning

46 alts after pruning (40 fresh and 6 done)

	Pruned	Kept	Total
New	429	23	452
Fresh	12	17	29
Picked	3	2	5
Done	1	4	5
Total	445	46	491

Accuracy

100.0%

Counts

491 → 46

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.5%	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	99.8%	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 2 binary64)))
	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
	98.7%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
	99.7%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
	99.6%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps))))) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	61.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.3%	(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
	61.2%	(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
	5.1%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	60.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
✓	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
	98.2%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	98.3%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	97.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	96.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
	98.0%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
	96.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
	6.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
	4.2%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
✓	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
✓	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))

Compiler

Compiled 3 485 to 1 831 computations (47.5% saved)

regimes70.0ms (0.9%)

Memory

-25.8MiB live, 113.2MiB allocated; 16ms collecting garbage

Counts

80 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
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(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 2 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps))))) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (.f64 (.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
(-.f64 (+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (.f64 (.f64 (.f64 eps eps) eps) (-.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (neg.f64 (/.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (.f64 (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) (/.f64 #s(literal 1 binary64) eps)) eps))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)))) (.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (.f64 (.f64 eps eps) (+.f64 (-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))) (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) eps))) eps))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (neg.f64 (.f64 (.f64 (.f64 eps eps) eps) (-.f64 (+.f64 #s(literal 1/6 binary64) (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 eps (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))))) eps)) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))))))

Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))

Outputs

(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))

Calls

3 calls:

23.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
21.0ms	x
18.0ms	eps

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes58.0ms (0.7%)

Memory

6.4MiB live, 105.2MiB allocated; 8ms collecting garbage

Counts

73 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
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(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps))))) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))

Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 2 binary64)))

Outputs

(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 2 binary64)))

Calls

3 calls:

19.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms	eps
17.0ms	x

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes53.0ms (0.6%)

Memory

-17.4MiB live, 73.6MiB allocated; 7ms collecting garbage

Counts

65 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 x (*.f64 #s(literal -1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)))) (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Outputs

(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))

Calls

3 calls:

16.0ms	eps
15.0ms	x
15.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes65.0ms (0.8%)

Memory

14.6MiB live, 58.9MiB allocated; 6ms collecting garbage

Counts

60 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 x (*.f64 #s(literal -1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)))) (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Outputs

(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Calls

3 calls:

34.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms	x
14.0ms	eps

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes59.0ms (0.7%)

Memory

6.8MiB live, 58.6MiB allocated; 23ms collecting garbage

Counts

58 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 x (*.f64 #s(literal -1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)))) (*.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))

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

Calls

3 calls:

29.0ms	x
13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	eps

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes144.0ms (1.8%)

Memory

-2.5MiB live, 43.4MiB allocated; 4ms collecting garbage

Counts

55 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 x (*.f64 #s(literal -1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x (.f64 #s(literal 4/3 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))

Outputs

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

Calls

3 calls:

115.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	x
13.0ms	eps

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes72.0ms (0.9%)

Memory

-7.8MiB live, 38.2MiB allocated; 4ms collecting garbage

Counts

54 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (-.f64 x (*.f64 #s(literal -1/3 binary64) eps))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
(/.f64 #s(approx (sin (- (+ eps x) x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))

Outputs

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

Calls

3 calls:

44.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	eps
12.0ms	x

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes37.0ms (0.5%)

Memory

12.5MiB live, 56.1MiB allocated; 6ms collecting garbage

Counts

43 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 eps (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))

Outputs

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

Calls

3 calls:

15.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	eps
10.0ms	x

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes35.0ms (0.4%)

Memory

27.9MiB live, 79.5MiB allocated; 9ms collecting garbage

Counts

39 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))

Outputs

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

Calls

3 calls:

14.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes30.0ms (0.4%)

Memory

-27.4MiB live, 65.5MiB allocated; 5ms collecting garbage

Counts

34 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))

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

Calls

3 calls:

11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	x
8.0ms	eps

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.7%	1	`eps`
98.7%	1	`x`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes28.0ms (0.3%)

Memory

22.4MiB live, 65.1MiB allocated; 7ms collecting garbage

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal 2/15 binary64) (.f64 #s(literal -17/315 binary64) (*.f64 eps eps))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x) eps (.f64 eps eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- (neg ( (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) #s(approx (neg (pow (tan x) 2)) (.f64 (fma.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (.f64 x (fma.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps)))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (fma.f64 eps x (*.f64 eps eps)))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))

Outputs

#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))

Calls

3 calls:

11.0ms	x
7.0ms	eps
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
98.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.3%	1	`x`
98.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes22.0ms (0.3%)

Memory

-17.2MiB live, 31.5MiB allocated; 16ms collecting garbage

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x eps #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (+ (* (cos (+ x x)) 1/2) 1/2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (+ (* (cos (+ x x)) 1/2) 1/2) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 eps eps (*.f64 eps x)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (neg (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) eps)) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ eps (* x (- 1 (* -4/3 (* eps eps)))))))) (.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))

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

Calls

3 calls:

13.0ms	x
4.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	eps

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes9.0ms (0.1%)

Memory

25.9MiB live, 26.0MiB allocated; 0ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	eps
3.0ms	x

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes11.0ms (0.1%)

Memory

-24.9MiB live, 19.9MiB allocated; 8ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	eps
2.0ms	x
2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
98.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.0%	1	`x`
98.0%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes5.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated; 0ms collecting garbage

Accuracy

Total -0.1b remaining (-2.7%)

Threshold costs -0.1b (-2.7%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))

Calls

3 calls:

2.0ms	x
2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	eps

Results

Accuracy	Segments	Branch
96.9%	1	`x`
96.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
96.9%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations582.0ms (7.1%)

Memory

-18.6MiB live, 597.5MiB allocated; 138ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 344 to 176 computations (48.8% saved)

preprocess187.0ms (2.3%)

Memory: 43.7MiB live, 223.7MiB allocated; 40ms collecting garbage
Compiler: Compiled 378 to 206 computations (45.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze27.0ms (0.3%)

sample4.6s (56.5%)

preprocess45.0ms (0.6%)

series12.0ms (0.1%)

rewrite194.0ms (2.4%)

eval14.0ms (0.2%)

prune12.0ms (0.1%)

series99.0ms (1.2%)

rewrite551.0ms (6.8%)

eval166.0ms (2%)

prune30.0ms (0.4%)

series75.0ms (0.9%)

rewrite300.0ms (3.7%)

eval68.0ms (0.8%)

prune36.0ms (0.4%)

series53.0ms (0.7%)

rewrite239.0ms (2.9%)

eval94.0ms (1.2%)

prune65.0ms (0.8%)

regimes70.0ms (0.9%)

regimes58.0ms (0.7%)

regimes53.0ms (0.6%)

regimes65.0ms (0.8%)

regimes59.0ms (0.7%)

regimes144.0ms (1.8%)

regimes72.0ms (0.9%)

regimes37.0ms (0.5%)

regimes35.0ms (0.4%)

regimes30.0ms (0.4%)

regimes28.0ms (0.3%)

regimes22.0ms (0.3%)

regimes9.0ms (0.1%)

regimes11.0ms (0.1%)

regimes5.0ms (0.1%)

derivations582.0ms (7.1%)

preprocess187.0ms (2.3%)

end0.0ms (0%)

Profiling