Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

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

analyze39.0ms (0.5%)

Memory

-17.2MiB live, 26.9MiB allocated; 10ms 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)

sample4.2s (54.9%)

Memory

82.4MiB live, 4 115.7MiB allocated; 979ms collecting garbage

Samples

2.0s	25 890×	0	invalid
799.0ms	5 537×	1	valid
172.0ms	2 719×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-tan: 666.0ms (36.9% of total)

adjust: 269.0ms (14.9% of total)

ival-fabs: 242.0ms (13.4% of total)

ival-add!: 178.0ms (9.9% of total)

ival-<: 145.0ms (8% of total)

ival-mult!: 130.0ms (7.2% of total)

ival-sub!: 94.0ms (5.2% of total)

ival-and: 67.0ms (3.7% of total)

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

Bogosity

preprocess29.0ms (0.4%)

Memory

17.5MiB live, 17.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	62	50
2	225	50
3	1487	50

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 12 to 12 computations (0% saved)

series12.0ms (0.2%)

Memory

9.2MiB live, 9.2MiB 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))

rewrite149.0ms (2%)

Memory

9.9MiB live, 108.8MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	1230
0	201	1091
1	1265	878
0	8316	848

Stop Event

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

Counts

37 → 82

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

eval10.0ms (0.1%)

Memory: -34.9MiB live, 10.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 1 080 to 401 computations (62.9% saved)

prune10.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	64	14	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	15	79

Accuracy

99.9%

Counts

79 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.9%	(/.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)))
▶	62.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶	4.9%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
▶	5.0%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
	8.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	8.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	60.7%	(-.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)))
	97.3%	#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)))
▶	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.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)) #s(literal -1/2 binary64) (/.f64 (fma.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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.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 1/6 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))))))))) 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))
	98.9%	#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))
	98.6%	#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))
	98.2%	#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))
▶	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))

Compiler

Compiled 640 to 458 computations (28.4% saved)

series142.0ms (1.9%)

Memory

13.3MiB live, 108.5MiB allocated; 14ms collecting garbage

Counts

59 → 294

Calls

Call 1

Inputs
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#s(literal 1/6 binary64)
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(.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))))
(.f64 #s(literal 1/6 binary64) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))
(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)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 eps)
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(tan.f64 (+.f64 (+.f64 x (PI.f64)) eps))
(+.f64 (+.f64 x (PI.f64)) eps)
(+.f64 x (PI.f64))
(PI.f64)
(-.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)
(-.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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (+ 1 (* 2/3 (pow eps 2))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))
#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) #s(hole binary64 (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))))
#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) #s(hole binary64 (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))))
#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) #s(hole binary64 (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))))
#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) #s(hole binary64 1/3))
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#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))))
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2))))))) 1/6)))
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#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
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#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
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#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
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#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)))
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#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)))
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#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
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#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
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#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
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Calls

6 calls:

Time	Variable		Point	Expression
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rewrite229.0ms (3%)

Memory

1.7MiB live, 186.8MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1608	26966
0	1725	23899
0	8377	23583

Stop Event

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

Counts

353 → 464

Calls

Call 1

Inputs
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2))))))) 1/6)))
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#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
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#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
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#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
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#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)))
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#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)))
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#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
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#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
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#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
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#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (- (/ (* (+ 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)))))) eps)) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x)))))))))
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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)))))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) #s(hole binary64 (/ (sin (- (+ x (* 2 (PI))) (* -1 eps))) (cos (- (+ x (* 2 (PI))) (* -1 eps))))))
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#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

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

eval95.0ms (1.3%)

Memory: 10.1MiB live, 97.7MiB allocated; 11ms collecting garbage
Compiler: Compiled 29 783 to 4 950 computations (83.4% saved)

prune34.0ms (0.4%)

Memory

-8.7MiB live, 38.1MiB allocated; 1ms collecting garbage

Pruning

30 alts after pruning (25 fresh and 5 done)

	Pruned	Kept	Total
New	421	19	440
Fresh	3	6	9
Picked	1	4	5
Done	0	1	1
Total	425	30	455

Accuracy

99.9%

Counts

455 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.9%	(/.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)))
✓	62.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	62.3%	(-.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))
	61.8%	(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	4.9%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)) (PI.f64))) (tan.f64 x))
✓	4.9%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
▶	7.7%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	5.0%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
	8.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	8.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.0%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.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)) #s(literal -1/2 binary64) (/.f64 (fma.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))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (neg.f64 (/.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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.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 1/6 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))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (neg.f64 (/.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))))))))) eps) (/.f64 (neg.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))
	98.6%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 eps (.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
	98.9%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1 binary64) (.f64 eps (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) (cos.f64 x)) (fma.f64 #s(literal -1/3 binary64) (tan.f64 x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (/.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))) (cos.f64 x)))))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))))) (.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))))
	3.2%	#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan.f64 (-.f64 eps (*.f64 #s(literal -2 binary64) (PI.f64)))))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 (+.f64 x (PI.f64))) #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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (+.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 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #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))))))))) 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))
	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- ( (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	97.8%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- ( (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 #s(literal 4/3 binary64) eps (.f64 x (-.f64 #s(literal 4/3 binary64) (.f64 #s(literal -17/9 binary64) (.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- ( (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))
▶	98.6%	#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))
	98.2%	#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))
▶	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))
	97.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps))) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
✓	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
▶	97.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))))))))
	97.2%	#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))))))))
	97.2%	#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 3 133 to 1 791 computations (42.8% saved)

series167.0ms (2.2%)

Memory

-10.6MiB live, 129.7MiB allocated; 39ms collecting garbage

Counts

74 → 343

Calls

Call 1

Inputs
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eps
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#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
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#s(approx (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* -1/6 x)))
#s(approx (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* -11/9 (pow x 2)) 1/6))))
#s(approx (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* (pow x 2) (- (* -197/90 (pow x 2)) 11/9)) 1/6))))
#s(approx (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2392/945 (pow x 2)) 197/90)) 11/9)) 1/6))))
#s(approx (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* -41/36 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -1141/720 (pow x 2)) 41/36)) 1/6))))
#s(approx (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -44981/30240 (pow x 2)) 1141/720)) 41/36)) 1/6))))
#s(approx (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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 (* (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 (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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 (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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 (* (- 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (- 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)))) #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 (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 -1))
#s(approx (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (- (* -2 (pow x 2)) 1)))
#s(approx (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (- (* (pow x 2) (- (* -7/3 (pow x 2)) 2)) 1)))
#s(approx (neg (/ (- 1 (neg (pow (tan x) 2))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -94/45 (pow x 2)) 7/3)) 2)) 1)))
#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 (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (pow x 2) 1/2)))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) 1/2)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#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 (neg (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (- (* -5/6 (pow x 2)) 1))))
#s(approx (neg (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -61/120 (pow x 2)) 5/6)) 1))))
#s(approx (neg (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -277/1008 (pow x 2)) 61/120)) 5/6)) 1))))
#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 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (* eps (- 1 (* -1/3 (pow eps 2))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* x (- 1 (* -4/3 (pow eps 2))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (+ (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* x (- (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (PI))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (+ x (PI)))))
#s(approx (+ x (PI)) #s(hole binary64 (PI)))
#s(approx (+ x (PI)) #s(hole binary64 (+ x (PI))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (/ (sin (PI)) (cos (PI)))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#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 (* eps x))))
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Calls

6 calls:

Time	Variable		Point	Expression
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rewrite262.0ms (3.4%)

Memory

34.8MiB live, 213.4MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1862	36879
0	1998	34351
0	8837	33762

Stop Event

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

Counts

417 → 510

Calls

Call 1

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

eval124.0ms (1.6%)

Memory: -15.8MiB live, 126.4MiB allocated; 19ms collecting garbage
Compiler: Compiled 35 150 to 5 555 computations (84.2% saved)

prune44.0ms (0.6%)

Memory

5.5MiB live, 52.2MiB allocated; 2ms collecting garbage

Pruning

47 alts after pruning (38 fresh and 9 done)

	Pruned	Kept	Total
New	463	24	487
Fresh	6	14	20
Picked	1	4	5
Done	0	5	5
Total	470	47	517

Accuracy

99.9%

Counts

517 → 47

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.9%	(/.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)))
✓	62.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	62.3%	(-.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))
	61.8%	(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	4.9%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)) (PI.f64))) (tan.f64 x))
✓	4.9%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
✓	7.7%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	5.0%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
	2.8%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) #s(approx (tan (+ x (PI))) #s(literal 0 binary64)))
	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
	8.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	8.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	98.9%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))) eps) (/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
	98.9%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))) eps) (/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
✓	99.0%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.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)) #s(literal -1/2 binary64) (/.f64 (fma.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))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (neg.f64 (/.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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.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 1/6 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))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (neg.f64 (/.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))))))))) eps) (/.f64 (neg.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))
	98.6%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 eps (.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
▶	98.9%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1 binary64) (.f64 eps (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) (cos.f64 x)) (fma.f64 #s(literal -1/3 binary64) (tan.f64 x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (/.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))) (cos.f64 x)))))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))))) (.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))))
	3.2%	#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan.f64 (-.f64 eps (*.f64 #s(literal -2 binary64) (PI.f64)))))
	98.6%	#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 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
✓	98.6%	#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))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶	97.6%	#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 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(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	97.6%	#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 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(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	97.8%	#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 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.0%	#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))
	98.2%	#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))
✓	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
	53.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) eps))
	6.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
	97.2%	#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))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal 5/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) eps))))))))) eps))
	97.3%	#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))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
	97.1%	#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))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
✓	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
▶	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (- 1 (* -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))))))))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (+ ( eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal 4/3 binary64) (/.f64 x eps)))))))))
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▶	97.2%	#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) eps))
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	97.2%	#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 5 102 to 3 064 computations (39.9% saved)

series158.0ms (2.1%)

Memory

-1.4MiB live, 138.1MiB allocated; 14ms collecting garbage

Counts

95 → 395

Calls

Call 1

Inputs
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eps
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#s(literal 1 binary64)
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#s(literal 1/3 binary64)
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#s(literal -1 binary64)
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(sin.f64 x)
x
(-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
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(/.f64 (-.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)))))
(-.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)
#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) (cos.f64 (.f64 #s(literal 2 binary64) x)))
#s(literal -1/2 binary64)
(cos.f64 x)
(fma.f64 #s(literal -1/3 binary64) (tan.f64 x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (/.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))) (cos.f64 x))))
#s(literal -1/3 binary64)
(tan.f64 x)
(fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (/.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))) (cos.f64 x)))
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
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(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
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(*.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
#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)
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Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
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#s(approx (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1/3 (pow x 2))))
#s(approx (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 (pow x 2)))
#s(approx (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (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))
#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 (- 1/2 (* -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 (* -1/2 (cos (* 2 x))) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (pow x 2) 1/2)))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) 1/2)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))) #s(hole binary64 (* -1/3 x)))
#s(approx (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))) #s(hole binary64 (* x (- (* -7/9 (pow x 2)) 1/3))))
#s(approx (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -77/45 (pow x 2)) 7/9)) 1/3))))
#s(approx (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2054/945 (pow x 2)) 77/45)) 7/9)) 1/3))))
#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 (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) #s(hole binary64 (* -2/3 (pow x 3))))
#s(approx (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) #s(hole binary64 (* (pow x 3) (- (* -5/3 (pow x 2)) 2/3))))
#s(approx (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* -97/45 (pow x 2)) 5/3)) 2/3))))
#s(approx (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -1184/567 (pow x 2)) 97/45)) 5/3)) 2/3))))
#s(approx (pow (tan x) 3) #s(hole binary64 (pow x 3)))
#s(approx (pow (tan x) 3) #s(hole binary64 (* (pow x 3) (+ 1 (pow x 2)))))
#s(approx (pow (tan x) 3) #s(hole binary64 (* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))))
#s(approx (pow (tan x) 3) #s(hole binary64 (* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))))
#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* -1/3 (pow x 3))))
#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* (pow x 3) (- (* -4/3 (pow x 2)) 1/3))))
#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* -86/45 (pow x 2)) 4/3)) 1/3))))
#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -1096/567 (pow x 2)) 86/45)) 4/3)) 1/3))))
#s(approx (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 3) (- (* -7/6 (pow x 2)) 1/3))))
#s(approx (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* -151/120 (pow x 2)) 7/6)) 1/3))))
#s(approx (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -9367/9072 (pow x 2)) 151/120)) 7/6)) 1/3))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1/3 (pow x 2))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -11/9 (pow x 2)) 1/3))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -197/135 (pow x 2)) 11/9)) 1/3))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1196/945 (pow x 2)) 197/135)) 11/9)) 1/3))))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (pow x 4)))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (* (pow x 4) (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))))
#s(approx (pow (sin x) 4) #s(hole binary64 (* (pow x 4) (+ 1 (* -2/3 (pow x 2))))))
#s(approx (pow (sin x) 4) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))))
#s(approx (pow (sin x) 4) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 5/3 (pow x 2)) 2)))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/3 (* -34/45 (pow x 2)))) 2)))))
#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))))
#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))))
#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* -4/3 (pow x 2))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 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))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1382/945 (pow x 2)) 248/135)) 17/9)) 4/3))))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* -1 x)))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (+ (tan x) (pow (tan x) 3)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (+ (tan x) (pow (tan x) 3)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (+ (tan x) (pow (tan x) 3)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 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 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (* eps (- 1 (* -1/3 (pow eps 2))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* eps x))))
#s(approx (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) #s(hole binary64 (+ x (* 1/3 eps))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))))
#s(approx (* eps (+ 1/3 (* 4/3 (* x x)))) #s(hole binary64 (+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))))
#s(approx (+ 1/3 (* 4/3 (* x x))) #s(hole binary64 (+ 1/3 (* 4/3 (pow x 2)))))
#s(approx (* 4/3 (* x x)) #s(hole binary64 (* 4/3 (pow x 2))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* x (- 1 (* -4/3 (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 (* 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))))))))
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Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	x	@	-inf	((- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (* eps (- (+ 1 (* eps (- (* eps (- (- 1/3 (* 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))))) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))))) (* -1 (+ (tan x) (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) eps (- (+ 1 (* eps (- (* eps (- (- 1/3 (* 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ 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rewrite498.0ms (6.6%)

Memory

27.2MiB live, 258.9MiB allocated; 54ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1988	38287
0	2150	34216
0	9027	33743

Stop Event

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

Counts

490 → 587

Calls

Call 1

Inputs
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eps
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(sin.f64 x)
x
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#s(literal 1/2 binary64)
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#s(literal 2 binary64)
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#s(literal -1/2 binary64)
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#s(literal -1/3 binary64)
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#s(literal 3 binary64)
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#s(literal 4 binary64)
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(.f64 #s(literal 4/3 binary64) (.f64 x x))
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#s(approx (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* -97/45 (pow x 2)) 5/3)) 2/3))))
#s(approx (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -1184/567 (pow x 2)) 97/45)) 5/3)) 2/3))))
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#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* -1/3 (pow x 3))))
#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* (pow x 3) (- (* -4/3 (pow x 2)) 1/3))))
#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* -86/45 (pow x 2)) 4/3)) 1/3))))
#s(approx (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -1096/567 (pow x 2)) 86/45)) 4/3)) 1/3))))
#s(approx (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 3) (- (* -7/6 (pow x 2)) 1/3))))
#s(approx (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* -151/120 (pow x 2)) 7/6)) 1/3))))
#s(approx (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -9367/9072 (pow x 2)) 151/120)) 7/6)) 1/3))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1/3 (pow x 2))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -11/9 (pow x 2)) 1/3))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -197/135 (pow x 2)) 11/9)) 1/3))))
#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1196/945 (pow x 2)) 197/135)) 11/9)) 1/3))))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (pow x 4)))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (* (pow x 4) (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))))
#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))))
#s(approx (pow (sin x) 4) #s(hole binary64 (* (pow x 4) (+ 1 (* -2/3 (pow x 2))))))
#s(approx (pow (sin x) 4) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))))
#s(approx (pow (sin x) 4) #s(hole binary64 (* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 5/3 (pow x 2)) 2)))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/3 (* -34/45 (pow x 2)))) 2)))))
#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))))
#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))))
#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* -4/3 (pow x 2))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 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))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1382/945 (pow x 2)) 248/135)) 17/9)) 4/3))))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* -1 x)))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (* -1 (+ (tan x) (pow (tan x) 3))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (+ (tan x) (pow (tan x) 3)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (+ (tan x) (pow (tan x) 3)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (+ (tan x) (pow (tan x) 3)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 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 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (* eps (- 1 (* -1/3 (pow eps 2))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* eps x))))
#s(approx (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) #s(hole binary64 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) #s(hole binary64 (+ x (* 1/3 eps))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))))
#s(approx (* eps (+ 1/3 (* 4/3 (* x x)))) #s(hole binary64 (+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))))
#s(approx (+ 1/3 (* 4/3 (* x x))) #s(hole binary64 (+ 1/3 (* 4/3 (pow x 2)))))
#s(approx (* 4/3 (* x x)) #s(hole binary64 (* 4/3 (pow x 2))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* x (- 1 (* -4/3 (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 (* 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 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))))) #s(hole binary64 (+ 1 (* 4/3 (pow x 2)))))
#s(approx (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2)))))))
#s(approx (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2)))))))))
#s(approx (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x)))))) #s(hole binary64 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
#s(approx (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x)))))) #s(hole binary64 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
#s(approx (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))) #s(hole binary64 4/3))
#s(approx (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))) #s(hole binary64 (+ 4/3 (* 17/15 (pow x 2)))))
#s(approx (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))) #s(hole binary64 (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2)))))))
#s(approx (* (* x x) (+ 17/15 (* 248/315 (* x x)))) #s(hole binary64 (* 17/15 (pow x 2))))
#s(approx (* (* x x) (+ 17/15 (* 248/315 (* x x)))) #s(hole binary64 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))
#s(approx (+ 17/15 (* 248/315 (* x x))) #s(hole binary64 17/15))
#s(approx (+ 17/15 (* 248/315 (* x x))) #s(hole binary64 (+ 17/15 (* 248/315 (pow x 2)))))
#s(approx (* 248/315 (* x x)) #s(hole binary64 (* 248/315 (pow x 2))))
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#s(approx (- 1/3 (* 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))))) #s(hole binary64 (* eps (+ (* -1 (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))) (* 1/3 (/ 1 eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
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#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 4) (+ (* -1 (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x))))) (* -1 (/ (+ (* -1 (- (/ (* (+ 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))))))) (* -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))) eps))))))
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Outputs
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#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) (pow.f64 x #s(literal 4 binary64)))
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#s(approx (/ (pow (sin x) 4) (pow (cos x) 4)) (.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 6/5 binary64) (.f64 #s(literal 848/945 binary64) (*.f64 x x)))))))))
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#s(approx (pow (cos x) 4) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 5/3 binary64) (.f64 x x)) #s(literal 2 binary64)))))
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#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -62/945 binary64) (.f64 x x)) #s(literal 17/135 binary64))) #s(literal 2/9 binary64))) #s(literal 1/3 binary64))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (.f64 #s(literal -4/3 binary64) (.f64 x x)))
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#s(approx (+ (tan x) (pow (tan x) 3)) (.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)))))))))
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#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps)
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#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps 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 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps))))))))
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#s(approx (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x)))
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#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))
#s(approx (* eps (+ 1/3 (* 4/3 (* x x)))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 #s(literal 4/3 binary64) (.f64 eps (*.f64 x x)))))
#s(approx (+ 1/3 (* 4/3 (* x x))) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x))))
#s(approx (* 4/3 (* x x)) (.f64 #s(literal 4/3 binary64) (.f64 x x)))
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#s(approx (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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(approx (/ (pow (sin x) 4) (pow (cos x) 4)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))
#s(approx (pow (sin x) 4) (pow.f64 (sin.f64 x) #s(literal 4 binary64)))
#s(approx (pow (cos x) 4) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
#s(approx (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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(approx (* -1 (+ (tan x) (pow (tan x) 3))) (*.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
#s(approx (+ (tan x) (pow (tan x) 3)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps (.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 #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)))))))) (cos.f64 x)) (/.f64 (-.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(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (fma.f64 eps (-.f64 (fma.f64 #s(literal -1 binary64) (.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.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 #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))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.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 #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))))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (-.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 #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)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.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)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #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))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (cos.f64 x))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #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))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) 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 #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)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.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))))))))) (/.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 #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))))))) (cos.f64 x))) (/.f64 (-.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(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 (.f64 x x) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps))) (/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))) x))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 (.f64 x x) (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps))) (+.f64 (/.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))) x)))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) (.f64 eps (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) (/.f64 (*.f64 eps eps) x))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) (.f64 (.f64 x x) (fma.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) (+.f64 (/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (.f64 x x)) (/.f64 (*.f64 eps eps) x)))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (/.f64 eps x)))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 eps x)))))))
#s(approx (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (/.f64 eps x))))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) (.f64 #s(literal 4/3 binary64) (.f64 eps (*.f64 x x))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) (.f64 (.f64 x x) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) (.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (/.f64 eps (*.f64 x x)) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x)))))
#s(approx (* eps (+ 1/3 (* 4/3 (* x x)))) (.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal 4/3 binary64) eps))))
#s(approx (+ 1/3 (* 4/3 (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 4/3 binary64) (.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (.f64 eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -4/3 binary64) (.f64 eps eps))) (/.f64 (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))) x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps (.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 #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)))))))) (cos.f64 x)) (/.f64 (-.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(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (.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 #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)))))))) (cos.f64 x))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (/.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 #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))))))) (cos.f64 x)))
#s(approx (* x (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x)))))))) (*.f64 #s(literal 248/315 binary64) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* x (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x)))))))) (.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 248/315 binary64) (.f64 #s(literal 17/15 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
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#s(approx (* x (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x)))))))) (.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 248/315 binary64) (fma.f64 #s(literal 17/15 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal 4/3 binary64) (pow.f64 x #s(literal 4 binary64))))))))
#s(approx (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))))) (*.f64 #s(literal 248/315 binary64) (pow.f64 x #s(literal 6 binary64))))
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#s(approx (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))))) (.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 248/315 binary64) (fma.f64 #s(literal 17/15 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 4/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
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#s(approx (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x))))) (*.f64 #s(literal 248/315 binary64) (pow.f64 x #s(literal 4 binary64))))
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#s(approx (+ 17/15 (* 248/315 (* x x))) (.f64 (.f64 x x) (+.f64 #s(literal 248/315 binary64) (.f64 #s(literal 17/15 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))))
#s(approx (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 #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(approx (pow (tan x) 2) (/.f64 (-.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(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (tan.f64 x)))
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#s(approx (- 1/3 (* 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))))) (.f64 eps (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) (cos.f64 x)) (fma.f64 #s(literal -1/3 binary64) (tan.f64 x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (/.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))) (cos.f64 x))))) (.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (tan.f64 x)))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.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 #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))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.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 #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))))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (-.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 #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)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.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)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #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))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)))) (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #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))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) 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 #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)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.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))))))))) (.f64 #s(literal -1 binary64) (/.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 #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))))))) (.f64 eps (cos.f64 x))))) eps)))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.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 #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))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.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 #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))))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (-.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 #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)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.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)))))))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #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))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)))) (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #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))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) 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 #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)))))) (.f64 #s(literal 1/6 binary64) (/.f64 (-.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))))))))) (.f64 #s(literal -1 binary64) (/.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 #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))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) eps))) eps)))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (.f64 #s(literal -4/3 binary64) (.f64 x x)) #s(literal 1/3 binary64)) eps) (.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (.f64 #s(literal -1 binary64) (/.f64 x eps))) #s(literal 1/3 binary64)) eps) (.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal -1 binary64) (/.f64 (-.f64 (.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) (.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x))) (*.f64 #s(literal -1 binary64) (/.f64 x eps))))))
#s(approx (* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)))) (.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x))) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) eps)) eps))))))
#s(approx (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) eps))) eps) (.f64 #s(literal 4/3 binary64) (.f64 x x))))))
#s(approx (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps))) eps) (.f64 #s(literal 4/3 binary64) (.f64 x x))))))
#s(approx (+ x (* eps (+ 1/3 (* 4/3 (* x x))))) (.f64 #s(literal -1 binary64) (.f64 eps (fma.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x))) (*.f64 #s(literal -1 binary64) (/.f64 x eps))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (.f64 #s(literal -1 binary64) (/.f64 x eps))) eps) (.f64 #s(literal 2/3 binary64) x))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (/.f64 (.f64 x x) eps)) eps))) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -4/3 binary64) x) (/.f64 #s(literal 1 binary64) eps)) eps)))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) eps))) eps)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (.f64 #s(literal -1 binary64) (.f64 eps (fma.f64 #s(literal -1 binary64) (/.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 #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))))))) (cos.f64 x)) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) eps))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (.f64 #s(literal -1 binary64) (.f64 eps (-.f64 (.f64 #s(literal -1 binary64) (/.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 #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))))))) (cos.f64 x))) (/.f64 #s(literal 1 binary64) eps)))))

eval119.0ms (1.6%)

Memory: 12.7MiB live, 154.7MiB allocated; 27ms collecting garbage
Compiler: Compiled 32 127 to 6 540 computations (79.6% saved)

prune72.0ms (1%)

Memory

-24.2MiB live, 68.2MiB allocated; 5ms collecting garbage

Pruning

48 alts after pruning (36 fresh and 12 done)

	Pruned	Kept	Total
New	481	10	491
Fresh	7	26	33
Picked	2	3	5
Done	0	9	9
Total	490	48	538

Accuracy

99.9%

Counts

538 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.9%	(/.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)))
✓	62.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	62.3%	(-.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))
	61.8%	(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	4.9%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)) (PI.f64))) (tan.f64 x))
✓	4.9%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
✓	7.7%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	5.0%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
	2.8%	(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) #s(approx (tan (+ x (PI))) #s(literal 0 binary64)))
	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
	8.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	8.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	62.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
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✓	99.0%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.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)) #s(literal -1/2 binary64) (/.f64 (fma.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))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (neg.f64 (/.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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.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 1/6 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))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (neg.f64 (/.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))))))))) eps) (/.f64 (neg.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))
	98.9%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 eps #s(approx (- (- 1/3 ( 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))))) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))))) (-.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (fma.f64 #s(literal -1/3 binary64) (/.f64 (-.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))))) (.f64 eps (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) (cos.f64 x)) (fma.f64 #s(literal -1/3 binary64) (tan.f64 x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (/.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal -1/3 binary64) (/.f64 (-.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)))))))) (cos.f64 x)))))))))))) (.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
	98.6%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) #s(approx ( eps (- (* eps (- (- 1/3 (* 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))))) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))))) (* -1 (+ (tan x) (pow (tan x) 3))))) (.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))))
	3.2%	#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan.f64 (-.f64 eps (*.f64 #s(literal -2 binary64) (PI.f64)))))
	98.6%	#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 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))
✓	98.6%	#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))
	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	97.8%	#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 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(approx (+ 4/3 ( (* x x) (+ 17/15 (* 248/315 (* x x))))) #s(literal 4/3 binary64)))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps #s(approx (/ ( (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(approx (* x (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x)))))))) (*.f64 #s(literal 248/315 binary64) (pow.f64 x #s(literal 7 binary64))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	98.0%	#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))
	98.2%	#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))
✓	97.2%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))
	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
	53.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) eps))
	6.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
	97.2%	#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))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal 5/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) eps))))))))) eps))
	97.3%	#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))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
	97.1%	#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))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
✓	97.1%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
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Compiler

Compiled 5 638 to 2 579 computations (54.3% saved)

regimes58.0ms (0.8%)

Memory

8.1MiB live, 58.3MiB allocated; 10ms collecting garbage

Counts

68 → 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))
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))) eps) (/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 (+.f64 x (PI.f64))) #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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #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 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (+.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 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 x (PI.f64))) #s(literal 2 binary64)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #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)) (sin.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #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 #s(literal 2 binary64) x)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))) eps) (/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) eps))

Outputs

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

Calls

3 calls:

22.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms	eps
15.0ms	x

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes83.0ms (1.1%)

Memory

-11.9MiB live, 80.2MiB allocated; 4ms collecting garbage

Counts

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

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

Outputs

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

Calls

3 calls:

28.0ms	eps
25.0ms	x
14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes46.0ms (0.6%)

Memory

35.8MiB live, 35.8MiB allocated; 0ms collecting garbage

Counts

61 → 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 (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x x))))))
#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))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 #s(literal 1/3 binary64) (.f64 eps 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))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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) (+.f64 eps (.f64 x (fma.f64 eps x (.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) #s(approx (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps #s(approx (+ 1 (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ x ( eps (+ 1/3 (* 4/3 (* x x))))) (+.f64 x (.f64 #s(literal 1/3 binary64) eps))) (.f64 x 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)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (+ ( eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
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#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- ( (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 #s(literal 4/3 binary64) eps (.f64 x (-.f64 #s(literal 4/3 binary64) (.f64 #s(literal -17/9 binary64) (.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 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 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.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))
#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))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) #s(approx ( eps (- (* eps (- (- 1/3 (* 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))))) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))))) (* -1 (+ (tan x) (pow (tan x) 3))))) (.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) 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))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 eps (.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #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)) (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 (+.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)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #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))))))))) 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)) (.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))

Outputs

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

Calls

3 calls:

14.0ms	x
14.0ms	eps
13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes49.0ms (0.6%)

Memory

3.8MiB live, 50.0MiB allocated; 2ms collecting garbage

Counts

59 → 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 (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x x))))))
#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))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 #s(literal 1/3 binary64) (.f64 eps 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))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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) (+.f64 eps (.f64 x (fma.f64 eps x (.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) #s(approx (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps #s(approx (+ 1 (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ x ( eps (+ 1/3 (* 4/3 (* x x))))) (+.f64 x (.f64 #s(literal 1/3 binary64) eps))) (.f64 x x)))))))
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#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 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(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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 #s(literal 4/3 binary64) eps (.f64 x (-.f64 #s(literal 4/3 binary64) (.f64 #s(literal -17/9 binary64) (.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 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 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.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))
#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))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) #s(approx ( eps (- (* eps (- (- 1/3 (* 1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x))) (+ (* -1/3 (tan x)) (+ (* -1/3 (pow (tan x) 3)) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (cos x)))))))) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))))) (* -1 (+ (tan x) (pow (tan x) 3))))) (.f64 eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) 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))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 eps (.f64 #s(literal -1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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 (+.f64 (+.f64 x (PI.f64)) (PI.f64))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #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)) (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 (+.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)))

Outputs

#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))

Calls

3 calls:

18.0ms	eps
13.0ms	x
13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
98.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.6%	1	`x`
98.6%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes46.0ms (0.6%)

Memory

4.3MiB live, 52.1MiB allocated; 9ms collecting garbage

Counts

52 → 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 (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x x))))))
#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))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 #s(literal 1/3 binary64) (.f64 eps 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))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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) (+.f64 eps (.f64 x (fma.f64 eps x (.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) #s(approx (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps #s(approx (+ 1 (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ x ( eps (+ 1/3 (* 4/3 (* x x))))) (+.f64 x (.f64 #s(literal 1/3 binary64) eps))) (.f64 x 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)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (+ ( eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ x ( eps (+ 1/3 (* 4/3 (* x x))))) (.f64 (.f64 x x) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x))))) (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps 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))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal 5/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) 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 (.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)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (+ ( eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 4 binary64))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (.f64 #s(literal -4/3 binary64) (.f64 x x)) #s(literal 1/3 binary64)) eps) (.f64 #s(literal 2/3 binary64) x))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan.f64 (-.f64 eps (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps 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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (- 1 (* -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) #s(approx (- 1 (* -2/3 (* eps eps))) (.f64 #s(literal 2/3 binary64) (.f64 eps eps)))))))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) #s(approx (tan (+ x (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (+ ( eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal 4/3 binary64) (/.f64 x eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (- 1 (* -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (+.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) (.f64 x (fma.f64 eps (.f64 x #s(approx (- 1 ( -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) #s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps 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))
#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 (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- ( (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))
#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 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (*.f64 x 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 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(approx (+ 4/3 ( (* x x) (+ 17/15 (* 248/315 (* x x))))) #s(literal 4/3 binary64)))))) #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))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 #s(approx (- ( (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.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)) #s(approx (* x (+ 1 (* (* x x) (+ 4/3 (* (* x x) (+ 17/15 (* 248/315 (* x x)))))))) (*.f64 #s(literal 248/315 binary64) (pow.f64 x #s(literal 7 binary64))))) #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 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(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (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 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(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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (.f64 eps eps) (.f64 x (fma.f64 #s(literal 4/3 binary64) eps (.f64 x (-.f64 #s(literal 4/3 binary64) (.f64 #s(literal -17/9 binary64) (.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 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 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.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))

Outputs

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

Calls

3 calls:

18.0ms	eps
12.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms	x

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)

regimes29.0ms (0.4%)

Memory

3.0MiB live, 45.5MiB allocated; 4ms collecting garbage

Counts

33 → 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))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (+.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) (.f64 x (fma.f64 eps (.f64 x #s(approx (- 1 ( -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) #s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps 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))
#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))

Outputs
#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))

Calls

3 calls:

11.0ms	eps
8.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

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)

regimes27.0ms (0.4%)

Memory

-11.3MiB live, 35.0MiB allocated; 2ms 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 (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x x))))))
#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))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 #s(literal 1/3 binary64) (.f64 eps 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))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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) (+.f64 eps (.f64 x (fma.f64 eps x (.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) #s(approx (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 eps x))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps #s(approx (+ 1 (+ ( eps (+ x (* eps (+ 1/3 (* 4/3 (* x x)))))) (* x x))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ x ( eps (+ 1/3 (* 4/3 (* x x))))) (+.f64 x (.f64 #s(literal 1/3 binary64) eps))) (.f64 x 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))))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps #s(approx (+ x ( eps (+ 1/3 (* 4/3 (* x x))))) (.f64 (.f64 x x) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 4/3 binary64) (.f64 x x))))) (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (*.f64 eps 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))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal 5/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) 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 (.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)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (+ ( eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 4 binary64))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (.f64 #s(literal -4/3 binary64) (.f64 x x)) #s(literal 1/3 binary64)) eps) (.f64 #s(literal 2/3 binary64) x))))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (tan.f64 (-.f64 eps (*.f64 #s(literal -2 binary64) (PI.f64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (fma.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps 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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (- 1 (* -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) #s(approx (- 1 (* -2/3 (* eps eps))) (.f64 #s(literal 2/3 binary64) (.f64 eps eps)))))))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) #s(approx (tan (+ x (PI))) #s(literal 0 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (+ ( eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal 4/3 binary64) (/.f64 x eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 #s(approx (- 1 (* -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (+.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) (.f64 x (fma.f64 eps (.f64 x #s(approx (- 1 ( -4/3 (* eps eps))) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))) (.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) #s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -2/3 binary64) (.f64 eps 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)))

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) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))

Calls

3 calls:

10.0ms	eps
7.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
97.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
97.3%	1	`x`
97.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes7.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms 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 (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x x))))))
#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))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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))) (.f64 #s(literal 1/3 binary64) (.f64 eps 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))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos 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))))))))) 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 (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
97.3%	1	`x`
97.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes5.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
97.3%	1	`x`
97.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes3.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 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))

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:

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

Results

Accuracy	Segments	Branch
97.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
97.2%	1	`x`
97.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations742.0ms (9.8%)

Memory

-144.0MiB live, 205.2MiB allocated; 1.0s collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 703 to 231 computations (67.1% saved)

preprocess134.0ms (1.8%)

Memory: -1.7MiB live, 238.3MiB allocated; 74ms collecting garbage
Compiler: Compiled 737 to 261 computations (64.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze39.0ms (0.5%)

sample4.2s (54.9%)

preprocess29.0ms (0.4%)

series12.0ms (0.2%)

rewrite149.0ms (2%)

eval10.0ms (0.1%)

prune10.0ms (0.1%)

series142.0ms (1.9%)

rewrite229.0ms (3%)

eval95.0ms (1.3%)

prune34.0ms (0.4%)

series167.0ms (2.2%)

rewrite262.0ms (3.4%)

eval124.0ms (1.6%)

prune44.0ms (0.6%)

series158.0ms (2.1%)

rewrite498.0ms (6.6%)

eval119.0ms (1.6%)

prune72.0ms (1%)

regimes58.0ms (0.8%)

regimes83.0ms (1.1%)

regimes46.0ms (0.6%)

regimes49.0ms (0.6%)

regimes46.0ms (0.6%)

regimes29.0ms (0.4%)

regimes27.0ms (0.4%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

derivations742.0ms (9.8%)

preprocess134.0ms (1.8%)

end0.0ms (0%)

Profiling