Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

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

analyze61.0ms (0.8%)

Memory

-3.2MiB live, 41.3MiB allocated; 9ms 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 (57.3%)

Memory

74.5MiB live, 4 208.5MiB allocated; 1.5s collecting garbage

Samples

1.8s	26 095×	0	invalid
1.1s	5 543×	1	valid
209.0ms	2 713×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-tan: 657.0ms (40.8% of total)

ival-fabs: 215.0ms (13.4% of total)

ival-<: 179.0ms (11.1% of total)

adjust: 139.0ms (8.6% of total)

ival-add!: 136.0ms (8.4% of total)

ival-mult!: 125.0ms (7.8% of total)

ival-sub!: 86.0ms (5.3% of total)

ival-and: 59.0ms (3.7% of total)

ival-assert: 13.0ms (0.8% of total)

Bogosity

explain87.0ms (1.2%)

Memory

16.1MiB live, 116.8MiB allocated; 7ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
216	3	(3.3961506672676903e-290 1.0107228080888544e-292)	1	(-3.269546009363942e-35 6.958630907816845e-37)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
1	0	-	0	-	`(tan.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`	cancellation	218	3
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	216	1
-	3	36

Precision

0.9863013698630136

Recall

0.9953917050691244

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	216	1	0
-	3	2	34

Precision?

0.9774774774774775

Recall?

1.0

Freqs

test

number	freq
0	37
1	219

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

35.0ms	352×	1	valid
7.0ms	158×	0	valid
0.0ms	2×	2	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-tan: 11.0ms (45.3% of total)

adjust: 8.0ms (32.9% of total)

ival-sub!: 3.0ms (12.3% of total)

ival-add!: 2.0ms (8.2% of total)

preprocess54.0ms (0.7%)

Memory

-21.5MiB live, 24.4MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	40	50
2	67	50
3	114	50
4	189	50
5	330	50
6	660	50
7	1513	50
8	2903	50
9	4334	50

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 14 to 12 computations (14.3% saved)

series12.0ms (0.2%)

Memory

15.9MiB live, 15.9MiB allocated; 0ms collecting garbage

Counts

6 → 36

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 (/ (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))
#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))
#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 (/ (sin x) (cos x))))
#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 eps #s(hole binary64 eps))
#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	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))
2.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))

rewrite195.0ms (2.6%)

Memory

11.1MiB live, 194.3MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	201	1262
0	206	1117
1	1269	904
0	8326	874

Stop Event

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

Counts

42 → 87

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

eval9.0ms (0.1%)

Memory: 16.1MiB live, 16.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 929 to 400 computations (79.3% saved)

prune25.0ms (0.3%)

Memory

-25.7MiB live, 19.8MiB allocated; 6ms collecting garbage

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	73	16	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	17	90

Accuracy

100.0%

Counts

90 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.0%	(/.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)))
▶	61.9%	(/.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))))
	61.9%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	62.0%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶	61.9%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	7.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	7.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	61.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	60.8%	(-.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)))
	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
▶	99.5%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (fma.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))) eps (.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64)) (.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
	99.3%	#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))
	99.1%	#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))
▶	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))

Compiler

Compiled 941 to 482 computations (48.8% saved)

series163.0ms (2.2%)

Memory

1.7MiB live, 148.6MiB allocated; 30ms collecting garbage

Counts

62 → 360

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 (fma.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))) eps (.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(.f64 (-.f64 (fma.f64 (fma.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))) eps (.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 (fma.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))) eps (.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))) eps (.f64 #s(literal 1 binary64) (/.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))
(fma.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))) eps (.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))))
(-.f64 (.f64 (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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64)))
(.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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))))
(neg.f64 eps)
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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
(sin.f64 x)
(cos.f64 x)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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))
(fma.f64 (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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))))
(+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))
(fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
#s(literal -1 binary64)
(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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(.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)))
(.f64 #s(literal 1 binary64) (/.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 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(.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)
(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))
(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))
(fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64))
#s(literal 17/315 binary64)
(*.f64 x x)
#s(literal 2/15 binary64)
#s(literal 1/3 binary64)
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
(cos.f64 (+.f64 eps 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 (.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
(*.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x)))
(neg.f64 (cos.f64 x))
(*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))
(neg.f64 (sin.f64 x))
(*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.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 (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) #s(hole binary64 1/3))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) #s(hole binary64 (+ 1/3 (* 2/3 (* eps x)))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* 2/3 (* eps x))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* 17/9 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2)))))))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* (pow x 2) (+ (* 124/45 eps) (* 2764/945 (* eps (pow x 2)))))))))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* -2/3 x)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* -17/9 (pow x 2)) 2/3))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #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))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -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 (* 1/6 (* (- 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 (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 x))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (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 (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow x 2)))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 2/15))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 (+ 2/15 (* 17/315 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (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 (- (/ (sin (+ eps x)) (cos (+ eps x))) (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 (/ (sin (+ eps x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) #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 (/ (sin (+ eps x)) (cos (+ eps x))) #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 (sin (+ eps x)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
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#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* -1 (sin eps))))
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#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (sin eps))))
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#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (sin eps)))))))
#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (* x (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))))
#s(approx (neg (cos x)) #s(hole binary64 -1))
#s(approx (neg (cos x)) #s(hole binary64 (- (* 1/2 (pow x 2)) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* -1 (* x (cos eps)))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* x (+ (* -1 (cos eps)) (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (* x (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))))))))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (* -1/3 (* x (sin eps)))))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (cos eps))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (sin eps)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (cos eps)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (cos eps) (* -1 (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (* 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 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 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* eps (+ (* eps (- (* -1 (* 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 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 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))))
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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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* -1 (* 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (+ (* -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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (/ (+ (* 1/6 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (+ (* 1/6 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* 17/315 (pow x 7))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* 17/315 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (* 17/315 (pow x 4))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (* (pow x 4) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 (* 17/315 (pow x 2))))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 (* (pow x 2) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 x))
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Calls

6 calls:

Time	Variable		Point	Expression
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rewrite248.0ms (3.4%)

Memory

10.8MiB live, 286.6MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1555	27409
0	1680	26401
0	8166	26124

Stop Event

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

Counts

422 → 530

Calls

Call 1

Inputs
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#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #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))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -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 (* 1/6 (* (- 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 (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 x))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (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 (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow x 2)))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 2/15))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 (+ 2/15 (* 17/315 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (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 (- (/ (sin (+ eps x)) (cos (+ eps x))) (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 (/ (sin (+ eps x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) #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 (/ (sin (+ eps x)) (cos (+ eps x))) #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 (sin (+ eps x)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* -1 (sin eps))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (+ (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* 1/20160 (sin eps)) (+ (* 1/720 (sin eps)) (* 1/576 (sin eps))))) (* -1 (+ (* 1/2520 (sin eps)) (* 1/360 (sin eps))))))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (sin eps))))
#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (sin eps)))))))
#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (* x (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))))
#s(approx (neg (cos x)) #s(hole binary64 -1))
#s(approx (neg (cos x)) #s(hole binary64 (- (* 1/2 (pow x 2)) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* -1 (* x (cos eps)))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* x (+ (* -1 (cos eps)) (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (* x (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))))))))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* x (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (* -1/3 (* x (sin eps)))))))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (cos eps))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (sin eps)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (cos eps)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (cos eps) (* -1 (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
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#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* -1 (* 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (+ (* -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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (/ (+ (* 1/6 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (cos x))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (+ (* 1/6 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* 17/315 (pow x 7))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* 17/315 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (* 17/315 (pow x 4))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(hole binary64 (* (pow x 4) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 (* 17/315 (pow x 2))))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(hole binary64 (* (pow x 2) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
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#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (sin (+ eps x))))))
#s(approx (neg (cos x)) #s(hole binary64 (* -1 (cos x))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* -1 (* (cos (+ eps x)) (sin x)))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (+ eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (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)))))
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#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- eps (* -1 x)))))
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#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
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#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (sin (- eps (* -1 x)))))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* -1 (* (cos (- eps (* -1 x))) (sin x)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* -1 (/ (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps)) eps))) 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))))))
#s(approx (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* (pow eps 2) (+ (* -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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))) (* -1 (/ (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) eps))))))
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#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)))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x)))) (* (cos x) (cos (- x (* -1 eps))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x))))))
#s(approx (* (sin (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (sin (- x (* -1 eps)))))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) #s(hole binary64 (* -1 (* (cos (- x (* -1 eps))) (sin x)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (- x (* -1 eps)))))))

Outputs
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#s(approx (neg (pow (tan x) 2)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -62/315 binary64) (.f64 x x)) #s(literal 17/45 binary64))) #s(literal 2/3 binary64))) #s(literal 1 binary64))))
#s(approx (pow (tan x) 2) (*.f64 x x))
#s(approx (pow (tan x) 2) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2/3 binary64) (.f64 x x)))))
#s(approx (pow (tan x) 2) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal 17/45 binary64) (.f64 x x)))))))
#s(approx (pow (tan x) 2) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 17/45 binary64) (.f64 #s(literal -62/315 binary64) (.f64 x x)))))))))
#s(approx (tan x) x)
#s(approx (tan x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))))
#s(approx (tan x) (.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)))))))
#s(approx (tan x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 #s(literal 17/315 binary64) (*.f64 x x)))))))))
#s(approx x x)
#s(approx (sin x) x)
#s(approx (sin x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
#s(approx (sin x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64))))))
#s(approx (sin x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 #s(literal -1/5040 binary64) (*.f64 x x)))) #s(literal 1/6 binary64))))))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))) #s(literal 1/2 binary64)))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) (*.f64 #s(literal -1/6 binary64) x))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) (.f64 x (-.f64 (.f64 #s(literal -11/9 binary64) (*.f64 x x)) #s(literal 1/6 binary64))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) (.f64 x (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -197/90 binary64) (*.f64 x x)) #s(literal 11/9 binary64))) #s(literal 1/6 binary64))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) (.f64 x (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -2392/945 binary64) (*.f64 x x)) #s(literal 197/90 binary64))) #s(literal 11/9 binary64))) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (*.f64 #s(literal -1/6 binary64) x))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (.f64 x (-.f64 (.f64 #s(literal -41/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (.f64 x (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1141/720 binary64) (*.f64 x x)) #s(literal 41/36 binary64))) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (.f64 x (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -44981/30240 binary64) (*.f64 x x)) #s(literal 1141/720 binary64))) #s(literal 41/36 binary64))) #s(literal 1/6 binary64))))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(literal -1/3 binary64))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (-.f64 (.f64 #s(literal -4/3 binary64) (.f64 x x)) #s(literal 1/3 binary64)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -17/9 binary64) (.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1/3 binary64)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -248/135 binary64) (.f64 x x)) #s(literal 17/9 binary64))) #s(literal 4/3 binary64))) #s(literal 1/3 binary64)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(literal -1/2 binary64))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) (-.f64 (.f64 #s(literal -4/3 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -17/9 binary64) (.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -248/135 binary64) (.f64 x x)) #s(literal 17/9 binary64))) #s(literal 4/3 binary64))) #s(literal 1/2 binary64)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) (*.f64 x x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 5/3 binary64) (.f64 x x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/3 binary64) (.f64 #s(literal 77/45 binary64) (.f64 x x)))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 77/45 binary64) (.f64 #s(literal 88/63 binary64) (.f64 x x)))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (*.f64 x x))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2/3 binary64) (.f64 x x)))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal 17/45 binary64) (.f64 x x)))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 17/45 binary64) (.f64 #s(literal -62/315 binary64) (.f64 x x)))))))))
#s(approx (pow (sin x) 2) (*.f64 x x))
#s(approx (pow (sin x) 2) (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))))
#s(approx (pow (sin x) 2) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 x x)) #s(literal 1/3 binary64))))))
#s(approx (pow (sin x) 2) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/45 binary64) (.f64 #s(literal -1/315 binary64) (.f64 x x)))) #s(literal 1/3 binary64))))))
#s(approx (pow (cos x) 2) #s(literal 1 binary64))
#s(approx (pow (cos x) 2) (+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x))))
#s(approx (pow (cos x) 2) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64)))))
#s(approx (pow (cos x) 2) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/45 binary64) (.f64 x x)))) #s(literal 1 binary64)))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(literal -1/2 binary64))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (-.f64 (.f64 #s(literal -1/3 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -2/9 binary64) (.f64 x x)) #s(literal 1/3 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -17/135 binary64) (.f64 x x)) #s(literal 2/9 binary64))) #s(literal 1/3 binary64))) #s(literal 1/2 binary64)))
#s(approx (* (pow (tan x) 2) 1/6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
#s(approx (* (pow (tan x) 2) 1/6) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal 1/9 binary64) (.f64 x x)))))
#s(approx (* (pow (tan x) 2) 1/6) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal 17/270 binary64) (.f64 x x)))))))
#s(approx (* (pow (tan x) 2) 1/6) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 17/270 binary64) (.f64 #s(literal 31/945 binary64) (.f64 x x)))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) (*.f64 #s(literal 1/6 binary64) x))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal 5/36 binary64) (*.f64 x x)))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/36 binary64) (.f64 #s(literal 61/720 binary64) (*.f64 x x)))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/36 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 61/720 binary64) (.f64 #s(literal 277/6048 binary64) (*.f64 x x)))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x)
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (*.f64 x x)))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4/3 binary64) (.f64 #s(literal 17/15 binary64) (*.f64 x x)))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 17/15 binary64) (.f64 #s(literal 248/315 binary64) (*.f64 x x)))))))))
#s(approx (tan (+ x eps)) (tan.f64 eps))
#s(approx (tan (+ x eps)) (fma.f64 x (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 (sin.f64 eps) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))) (cos.f64 eps))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal -1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))) (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (cos.f64 eps)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (tan.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) x)
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (.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)))))))
#s(approx (* (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 #s(literal 17/315 binary64) (*.f64 x x)))))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) #s(literal 1 binary64))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (.f64 x x))))))
#s(approx (+ (* (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (* x x)) 1) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 #s(literal 17/315 binary64) (.f64 x x))))))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) #s(literal 1/3 binary64))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (.f64 x x))))
#s(approx (+ (* (+ (* 17/315 (* x x)) 2/15) (* x x)) 1/3) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 #s(literal 17/315 binary64) (.f64 x x))))))
#s(approx (+ (* 17/315 (* x x)) 2/15) #s(literal 2/15 binary64))
#s(approx (+ (* 17/315 (* x x)) 2/15) (+.f64 #s(literal 2/15 binary64) (.f64 #s(literal 17/315 binary64) (.f64 x x))))
#s(approx (* x x) (*.f64 x x))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (tan.f64 eps))
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#s(approx (neg (cos x)) #s(literal -1 binary64))
#s(approx (neg (cos x)) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))
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#s(approx (* (cos (+ eps x)) (neg (sin x))) (.f64 x (fma.f64 #s(literal -1 binary64) (cos.f64 eps) (.f64 x (sin.f64 eps)))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) (.f64 x (fma.f64 #s(literal -1 binary64) (cos.f64 eps) (.f64 x (+.f64 (sin.f64 eps) (neg.f64 (.f64 x (.f64 (cos.f64 eps) #s(literal -2/3 binary64)))))))))
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#s(approx (neg (sin x)) (neg.f64 x))
#s(approx (neg (sin x)) (.f64 x (-.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1 binary64))))
#s(approx (neg (sin x)) (.f64 x (-.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x)))) #s(literal 1 binary64))))
#s(approx (neg (sin x)) (.f64 x (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/5040 binary64) (*.f64 x x)) #s(literal 1/120 binary64))))) #s(literal 1 binary64))))
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#s(approx (* (cos (+ eps x)) (neg (cos x))) (fma.f64 #s(literal -1 binary64) (cos.f64 eps) (.f64 x (+.f64 (sin.f64 eps) (.f64 x (cos.f64 eps))))))
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#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
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#s(approx (neg eps) (neg.f64 eps))
#s(approx eps eps)
#s(approx (tan eps) eps)
#s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
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#s(approx (tan (+ x eps)) (tan.f64 x))
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#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) (tan.f64 x))
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#s(approx (sin (+ eps x)) (sin.f64 x))
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#s(approx (cos (+ eps x)) (cos.f64 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (cos.f64 x)))) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x))))))))
#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal -1 binary64) (+.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (/.f64 (-.f64 (neg.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (pow.f64 eps #s(literal -1 binary64))) eps))) eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x))))))))
#s(approx (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (.f64 (.f64 eps eps) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)))) (neg.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (cos.f64 x))) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) eps)))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) (neg.f64 (.f64 eps (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal -1 binary64)) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)))))))))))
#s(approx (tan (+ x eps)) (tan.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ x eps) (neg.f64 (*.f64 eps (-.f64 (neg.f64 (/.f64 x eps)) #s(literal 1 binary64)))))
#s(approx (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (-.f64 (tan.f64 (-.f64 x (neg.f64 eps))) (tan.f64 x)))
#s(approx (/ (sin (+ eps x)) (cos (+ eps x))) (tan.f64 (-.f64 x (neg.f64 eps))))
#s(approx (sin (+ eps x)) (sin.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ eps x) (neg.f64 (*.f64 eps (-.f64 (neg.f64 (/.f64 x eps)) #s(literal 1 binary64)))))
#s(approx (cos (+ eps x)) (cos.f64 (-.f64 x (neg.f64 eps))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (-.f64 (.f64 (cos.f64 x) (sin.f64 (-.f64 x (neg.f64 eps)))) (.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))) (.f64 (cos.f64 x) (cos.f64 (-.f64 x (neg.f64 eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (.f64 #s(literal -1 binary64) (-.f64 (.f64 (cos.f64 x) (sin.f64 (-.f64 x (neg.f64 eps)))) (*.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))))
#s(approx (* (sin (+ eps x)) (neg (cos x))) (neg.f64 (*.f64 (cos.f64 x) (sin.f64 (-.f64 x (neg.f64 eps))))))
#s(approx (* (cos (+ eps x)) (neg (sin x))) (neg.f64 (*.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) (neg.f64 (*.f64 (cos.f64 x) (cos.f64 (-.f64 x (neg.f64 eps))))))

eval226.0ms (3.1%)

Memory: 28.3MiB live, 358.6MiB allocated; 48ms collecting garbage
Compiler: Compiled 138 832 to 7 532 computations (94.6% saved)

prune30.0ms (0.4%)

Memory

-32.3MiB live, 65.1MiB allocated; 6ms collecting garbage

Pruning

19 alts after pruning (15 fresh and 4 done)

	Pruned	Kept	Total
New	1 168	11	1 179
Fresh	7	4	11
Picked	2	3	5
Done	0	1	1
Total	1 177	19	1 196

Accuracy

100.0%

Counts

1 196 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.0%	(/.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)))
▶	99.9%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	62.0%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	61.9%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	7.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	7.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	61.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	99.2%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))
▶	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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 #s(approx (- (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))
▶	98.4%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))
	98.4%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
✓	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
▶	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
	98.4%	#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))))))))))
	98.4%	#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))))))))
▶	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))

Compiler

Compiled 2 487 to 974 computations (60.8% saved)

series137.0ms (1.9%)

Memory

43.1MiB live, 135.0MiB allocated; 9ms collecting garbage

Counts

46 → 263

Calls

Call 1

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

Outputs
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* -1 (sin eps))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (+ (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* 1/20160 (sin eps)) (+ (* 1/720 (sin eps)) (* 1/576 (sin eps))))) (* -1 (+ (* 1/2520 (sin eps)) (* 1/360 (sin eps))))))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (cos eps))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (sin eps)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (cos eps)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (cos eps) (* -1 (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (neg (cos x)) #s(hole binary64 -1))
#s(approx (neg (cos x)) #s(hole binary64 (- (* 1/2 (pow x 2)) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (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)))))
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#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
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#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
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#s(approx (neg (sin eps)) #s(hole binary64 (* -1 eps)))
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#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
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#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (* (cos x) (sin x))))))
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#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
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#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (tan eps) #s(hole binary64 eps))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
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#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* 2/3 (* eps eps))))))) #s(hole binary64 1))
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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))))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x)))))
#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 (* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x)))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) eps)) (* 2/3 x)))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x)))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/3 (* -1 (/ (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))) eps))))))
#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/2 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* 1/6 (/ 1 eps)) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* -1 (/ (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps)) eps))) 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))))))

Calls

6 calls:

Time	Variable		Point	Expression
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rewrite275.0ms (3.7%)

Memory

2.9MiB live, 330.0MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1297	20660
0	1357	19716
0	8421	18666

Stop Event

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

Counts

309 → 430

Calls

Call 1

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

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

eval85.0ms (1.2%)

Memory: -4.4MiB live, 189.8MiB allocated; 31ms collecting garbage
Compiler: Compiled 84 009 to 2 952 computations (96.5% saved)

prune28.0ms (0.4%)

Memory

-20.6MiB live, 72.9MiB allocated; 5ms collecting garbage

Pruning

23 alts after pruning (18 fresh and 5 done)

	Pruned	Kept	Total
New	516	15	531
Fresh	7	3	10
Picked	4	1	5
Done	0	4	4
Total	527	23	550

Accuracy

100.0%

Counts

550 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.2%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 (+.f64 eps (PI.f64)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
▶	100.0%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (neg.f64 (cos.f64 x))))
	99.9%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
▶	99.7%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	99.4%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	99.8%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	62.0%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	61.9%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	7.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	7.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	61.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
	98.4%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
✓	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
▶	98.4%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
▶	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
▶	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) eps))))
	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
✓	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))

Compiler

Compiled 3 281 to 1 347 computations (58.9% saved)

series102.0ms (1.4%)

Memory

23.5MiB live, 120.4MiB allocated; 8ms collecting garbage

Counts

52 → 242

Calls

Call 1

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

Outputs
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* -1 (sin eps))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (+ (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* 1/20160 (sin eps)) (+ (* 1/720 (sin eps)) (* 1/576 (sin eps))))) (* -1 (+ (* 1/2520 (sin eps)) (* 1/360 (sin eps))))))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (* -1 (cos eps))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (sin eps)))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (cos eps)))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (cos eps) (* -1 (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (cos eps)))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (sin eps))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (neg (cos x)) #s(hole binary64 -1))
#s(approx (neg (cos x)) #s(hole binary64 (- (* 1/2 (pow x 2)) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)))
#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+ (* 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 x) 1) eps) #s(hole binary64 eps))
#s(approx (* (+ (* x x) 1) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (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 eps) #s(hole binary64 (* eps x)))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* 2/3 (pow eps 4))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (+ (* 2/3 (pow eps 4)) (* 4/3 (* (pow eps 3) x)))))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 2/3))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 (+ 2/3 (* 4/3 (/ x eps)))))
#s(approx (/ x eps) #s(hole binary64 (/ x eps)))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (cos eps))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (sin eps)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (cos eps)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (cos eps) (* -1 (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x)))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (* (cos eps) (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* (sin eps) (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (neg (cos x)) #s(hole binary64 (* -1 (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (* 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 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 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (+ (* 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 (* (pow x 2) (+ 1 (* 4/3 (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 (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
#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 (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))))
#s(approx (* (+ (* x x) 1) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* (+ (* x x) 1) eps) #s(hole binary64 (* (pow x 2) (+ eps (/ eps (pow x 2))))))
#s(approx (+ (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
#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)))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* 4/3 (* (pow eps 3) x))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* x (+ (* 2/3 (/ (pow eps 4) x)) (* 4/3 (pow eps 3))))))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 (* 4/3 (/ x eps))))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 (* x (+ (* 4/3 (/ 1 eps)) (* 2/3 (/ 1 x))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x)))) (* (cos x) (cos (+ eps x)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (+ eps x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x)))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin 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 (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* -1 (* x (+ (* -4/3 (pow eps 3)) (* -2/3 (/ (pow eps 4) x)))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x)))) (* (cos x) (cos (- eps (* -1 x))))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* -1 (/ (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (* eps (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))) (pow (cos x) 3))) (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (* eps (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3)))))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* eps (+ (* -1 (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (* -1 (/ (* (sin x) (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* 1/6 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))))))))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (* -1/120 (pow (cos x) 2)) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* eps (- (+ (* -1 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* 1/6 (pow (cos x) 2)) (* (pow eps 2) (- (+ (* -1/120 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/5040 (pow (cos x) 2)) (* -1/5040 (pow (sin x) 2))))) (* 1/120 (pow (sin x) 2))))) (* -1/6 (pow (sin x) 2))))) (pow (sin x) 2)))))
#s(approx (neg (sin eps)) #s(hole binary64 (* -1 eps)))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* 1/6 (pow eps 2)) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2)))) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))) 1))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (* -1 (pow (cos x) 2))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (* (cos x) (sin x))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (+ (* 1/2 (* eps (pow (cos x) 2))) (* (cos x) (sin x)))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (+ (* eps (+ (* -1/6 (* eps (* (cos x) (sin x)))) (* 1/2 (pow (cos x) 2)))) (* (cos x) (sin x)))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (cos x)))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (sin x))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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Calls

6 calls:

Time	Variable		Point	Expression
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28.0ms	x	@	-inf	((/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg (sin eps)) (sin eps) eps (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (* (cos eps) (cos x)) (cos eps) (cos x) x (* (sin eps) (sin x)) (sin x) (neg (cos x)) (- (tan (+ x eps)) (tan x)) (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) (* (+ (* x x) 1) eps) (+ (* x x) 1) 1 (- (tan (+ x eps)) (tan x)) (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) (+ 1 (* 1/3 (* eps eps))) (* 1/3 (* eps eps)) 1/3 (* eps eps) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (* x eps) (- (tan (+ x eps)) (tan x)) (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (+ (* (/ x eps) 4/3) 2/3) (/ x eps) 4/3 2/3 (pow eps 4) 4 (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg (sin eps)) (sin eps) (* (+ (* -1/6 (* eps eps)) 1) eps) (+ (* -1/6 (* eps eps)) 1) -1/6 (* (cos (+ eps x)) (neg (cos x))) (cos (+ eps x)) (+ eps x))
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rewrite238.0ms (3.2%)

Memory

-21.0MiB live, 310.6MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1200	13356
0	1254	12433
1	7579	12433
0	8025	11739

Stop Event

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

Counts

294 → 439

Calls

Call 1

Inputs
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (neg.f64 (cos.f64 x))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps)))
(neg.f64 (sin.f64 eps))
(sin.f64 eps)
eps
(.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos.f64 eps)
(cos.f64 x)
x
(*.f64 (sin.f64 eps) (sin.f64 x))
(sin.f64 x)
(neg.f64 (cos.f64 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) eps))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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 (fma.f64 x x #s(literal 1 binary64)) eps))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 binary64)
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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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps)))))
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(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
#s(literal 1/3 binary64)
(*.f64 eps eps)
(.f64 x #s(approx (+ ( eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (*.f64 x eps)))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (*.f64 x eps))
(*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64)))))))
(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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))
(.f64 x #s(approx (+ ( eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64)))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64)))
(fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64))
(/.f64 x eps)
#s(literal 4/3 binary64)
#s(literal 2/3 binary64)
(pow.f64 eps #s(literal 4 binary64))
#s(literal 4 binary64)
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))))
(neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
#s(literal -1/6 binary64)
(*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x)))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* -1 (sin eps))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (+ (* -1 (sin eps)) (* (pow x 4) (- (+ (* -1 (+ (* 1/12 (sin eps)) (* 1/4 (sin eps)))) (* (pow x 2) (- (+ (* -1 (+ (* -1/24 (sin eps)) (* -1/360 (sin eps)))) (* (pow x 2) (- (* -1 (+ (* 1/20160 (sin eps)) (+ (* 1/720 (sin eps)) (* 1/576 (sin eps))))) (* -1 (+ (* 1/2520 (sin eps)) (* 1/360 (sin eps))))))) (* -1 (+ (* -1/36 (sin eps)) (* -1/60 (sin eps))))))) (* -1/3 (sin eps)))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (* -1 (cos eps))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (sin eps)))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (cos eps)))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (cos eps) (* -1 (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (cos eps)))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (sin eps))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (neg (cos x)) #s(hole binary64 -1))
#s(approx (neg (cos x)) #s(hole binary64 (- (* 1/2 (pow x 2)) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)))
#s(approx (neg (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)))
#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+ (* 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 x) 1) eps) #s(hole binary64 eps))
#s(approx (* (+ (* x x) 1) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ (* x x) 1) #s(hole binary64 1))
#s(approx (+ (* x x) 1) #s(hole binary64 (+ 1 (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 eps) #s(hole binary64 (* eps x)))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* 2/3 (pow eps 4))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (+ (* 2/3 (pow eps 4)) (* 4/3 (* (pow eps 3) x)))))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 2/3))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 (+ 2/3 (* 4/3 (/ x eps)))))
#s(approx (/ x eps) #s(hole binary64 (/ x eps)))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (+ (* x (+ (* x (+ (* x (+ (* -1 (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3)))) (cos eps)) (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (/ (sin eps) (cos eps)) (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (cos eps))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (sin eps)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (cos eps)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (cos eps)) (* x (+ (sin eps) (* x (+ (cos eps) (* -1 (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x)))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x))))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (- (* (cos eps) (cos x)) (* (sin eps) (sin x)))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (* (cos eps) (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* (sin eps) (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (neg (cos x)) #s(hole binary64 (* -1 (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (* 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 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 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (+ (* 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 (* (pow x 2) (+ 1 (* 4/3 (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 (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
#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 (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))))
#s(approx (* (+ (* x x) 1) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* (+ (* x x) 1) eps) #s(hole binary64 (* (pow x 2) (+ eps (/ eps (pow x 2))))))
#s(approx (+ (* x x) 1) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) 1) #s(hole binary64 (* (pow x 2) (+ 1 (/ 1 (pow x 2))))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
#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)))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* 4/3 (* (pow eps 3) x))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* x (+ (* 2/3 (/ (pow eps 4) x)) (* 4/3 (pow eps 3))))))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 (* 4/3 (/ x eps))))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 (* x (+ (* 4/3 (/ 1 eps)) (* 2/3 (/ 1 x))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (+ eps x)))) (* -1 (* (cos (+ eps x)) (sin x)))) (* (cos x) (cos (+ eps x)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (+ eps x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x)))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin 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 (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* -1 (* x (+ (* -4/3 (pow eps 3)) (* -2/3 (/ (pow eps 4) x)))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (- eps (* -1 x))))) (* -1 (* (cos (- eps (* -1 x))) (sin x)))) (* (cos x) (cos (- eps (* -1 x))))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* -1 (/ (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (* eps (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))) (pow (cos x) 3))) (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (* eps (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3)))))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* eps (+ (* -1 (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (* -1 (/ (* (sin x) (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* 1/6 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))))))))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))))
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#s(approx (neg (sin eps)) #s(hole binary64 (* -1 eps)))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* 1/6 (pow eps 2)) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2)))) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))) 1))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (* -1 (pow (cos x) 2))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (* (cos x) (sin x))))))
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#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (cos x)))
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#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos x)))
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#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (sin x))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))))
#s(approx (* (sin eps) (sin x)) #s(hole binary64 (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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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))))))) #s(hole binary64 (* eps (+ 1 (pow x 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 (+ (* eps x) (pow x 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 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 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 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))))))
#s(approx (* (+ (* x x) 1) eps) #s(hole binary64 (* eps (+ 1 (pow x 2)))))
#s(approx (+ 1 (* 1/3 (* eps eps))) #s(hole binary64 1))
#s(approx (+ 1 (* 1/3 (* eps eps))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (* 1/3 (* eps eps)) #s(hole binary64 (* 1/3 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* eps (+ (* eps x) (pow x 2)))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* eps (+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2)))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* eps (+ (* eps (+ x (* eps (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2)))))) (pow x 2)))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* eps x)))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* eps (+ eps x))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* eps (+ x (* eps (+ 1 (* 4/3 (* eps x))))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* eps (+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x)))))))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* (pow eps 3) (+ (* 2/3 eps) (* 4/3 x)))))
#s(approx (+ (* (/ x eps) 4/3) 2/3) #s(hole binary64 (/ (+ (* 2/3 eps) (* 4/3 x)) eps)))
#s(approx (pow eps 4) #s(hole binary64 (pow eps 4)))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* -1 (/ (* eps (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 2)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (* eps (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)))) (pow (cos x) 3))) (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (* eps (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3)))))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* eps (+ (* -1 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* eps (+ (* -1 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* eps (+ (* -1 (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* eps (+ (* -1 (/ (* (sin x) (- 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 4))) (+ (* -1/2 (/ (- (* -1 (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))) (* 1/6 (/ (* (sin x) (- (* -1 (pow (cos x) 2)) (pow (sin x) 2))) (pow (cos x) 3))))))))))))))
#s(approx (* (+ (* -1/6 (* eps eps)) 1) eps) #s(hole binary64 eps))
#s(approx (* (+ (* -1/6 (* eps eps)) 1) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (+ (* -1/6 (* eps eps)) 1) #s(hole binary64 1))
#s(approx (+ (* -1/6 (* eps eps)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (* (cos x) (sin x))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (+ (* 1/2 (* eps (pow (cos x) 2))) (* (cos x) (sin x)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (+ (* -1 (pow (cos x) 2)) (* eps (+ (* eps (+ (* -1/6 (* eps (* (cos x) (sin x)))) (* 1/2 (pow (cos x) 2)))) (* (cos x) (sin x)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (neg (sin eps)) #s(hole binary64 (* -1 (sin eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (cos eps) #s(hole binary64 (cos 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))) (+ (* -1 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 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 (* 2/3 (* (pow eps 4) x))))
#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 (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 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 (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (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 (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))))
#s(approx (+ 1 (* 1/3 (* eps eps))) #s(hole binary64 (* 1/3 (pow eps 2))))
#s(approx (+ 1 (* 1/3 (* eps eps))) #s(hole binary64 (* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2))))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* 2/3 (* (pow eps 4) x))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ x (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 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* 2/3 (pow eps 4))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2)))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))))))))
#s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) #s(hole binary64 (* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps))))))
#s(approx (* (+ (* -1/6 (* eps eps)) 1) eps) #s(hole binary64 (* -1/6 (pow eps 3))))
#s(approx (* (+ (* -1/6 (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ (* -1/6 (* eps eps)) 1) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* -1/6 (* eps eps)) 1) #s(hole binary64 (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x)))) (* (cos x) (- (* (cos eps) (cos x)) (* (sin eps) (sin x))))))))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(hole binary64 (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))) (* -1 (/ (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) eps))))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))) (* -1 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos 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)) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos 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))))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1/3) eps)) (* 2/3 x)))))
#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 (* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x)))))
#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 (* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x)))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) eps)) (* 2/3 x)))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x)))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps))))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 4) (+ 2/3 (* -1 (/ (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))) eps))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (neg (cos x)))) #s(hole binary64 (* -1 (/ (- (* -1 (* (cos x) (sin (- x (* -1 eps))))) (* -1 (* (cos (- x (* -1 eps))) (sin x)))) (* (cos x) (cos (- x (* -1 eps))))))))
#s(approx (* (+ (* -1/6 (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))))
#s(approx (* (cos (+ eps x)) (neg (cos x))) #s(hole binary64 (* -1 (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
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Outputs
(/.f64 (/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x)))
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(*.f64 (sin.f64 eps) #s(literal -1 binary64))
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(neg.f64 (sin.f64 eps))
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(cos.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 eps)
eps
(.f64 (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal -1 binary64))
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x
(*.f64 (sin.f64 eps) (sin.f64 x))
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#s(approx (sin x) x)
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#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (cos.f64 (+.f64 x eps)))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
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#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (.f64 #s(literal -1 binary64) (-.f64 (.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x)) (*.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 eps (neg.f64 x))) (tan.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 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 2/3 binary64) #s(literal 1 binary64)) (.f64 eps eps) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) eps) x))) x))) (.f64 x x)))
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#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (cos.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) (neg.f64 (*.f64 eps (/.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) (.f64 (.f64 #s(literal -1 binary64) (fma.f64 eps (/.f64 (*.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) (.f64 (fma.f64 (fma.f64 (neg.f64 eps) (-.f64 #s(literal 1/6 binary64) (fma.f64 (/.f64 (.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) eps (neg.f64 (/.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))
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#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (*.f64 (-.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (.f64 (-.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (.f64 (-.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 #s(literal -1/120 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 eps eps) (.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 eps eps) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (.f64 (-.f64 (fma.f64 (-.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/5040 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 eps eps) (.f64 #s(literal -1/120 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1/120 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (.f64 eps eps) (.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps))
#s(approx (neg (sin eps)) (neg.f64 eps))
#s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))
#s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/5040 binary64) (.f64 eps eps)) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx eps eps)
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) (fma.f64 (*.f64 (cos.f64 x) eps) (sin.f64 x) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (sin.f64 x) (cos.f64 x))) eps (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (.f64 (sin.f64 x) (cos.f64 x))) eps (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (cos.f64 x))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (* (cos eps) (cos x)) (cos.f64 x))
#s(approx (* (cos eps) (cos x)) (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (cos.f64 x)))
#s(approx (* (cos eps) (cos x)) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps) (cos.f64 x)))
#s(approx (* (cos eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/720 binary64)) (cos.f64 x) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps) (cos.f64 x)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (* (sin eps) (sin x)) (*.f64 (sin.f64 x) eps))
#s(approx (* (sin eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 eps eps) (sin.f64 x)) #s(literal -1/6 binary64) (sin.f64 x)) eps))
#s(approx (* (sin eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal 1/120 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) (*.f64 eps eps) (sin.f64 x)) eps))
#s(approx (* (sin eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal -1/5040 binary64) (.f64 #s(literal 1/120 binary64) (sin.f64 x))) (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (sin.f64 x))) (*.f64 eps eps) (sin.f64 x)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (.f64 (sin.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps))
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#s(approx (sin eps) (sin.f64 eps))
#s(approx (cos eps) (cos.f64 eps))
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#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 x (neg.f64 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (.f64 (.f64 #s(literal -1 binary64) (+.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (cos.f64 x)) (.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/6 binary64)))) (/.f64 (+.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (.f64 (cos.f64 x) eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (.f64 (fma.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (neg.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 (/.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 eps #s(literal -1 binary64))) eps) #s(literal -1 binary64) (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps) #s(literal -1 binary64) (neg.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (cos.f64 x)) (.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1/6 binary64)))))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) (.f64 (fma.f64 #s(literal 2/3 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 #s(literal -4/3 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) (.f64 (fma.f64 #s(literal 2/3 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (/.f64 (neg.f64 x) eps)) #s(literal 1/3 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))))) (.f64 (fma.f64 #s(literal 2/3 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (neg.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64)) eps) #s(literal -1 binary64) x) eps))) #s(literal 1/3 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) (.f64 (fma.f64 #s(literal 2/3 binary64) x (neg.f64 (/.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (/.f64 (neg.f64 x) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* x (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps)))))) (.f64 (fma.f64 #s(literal 2/3 binary64) x (neg.f64 (/.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 x x) (neg.f64 (/.f64 (+.f64 (/.f64 (*.f64 x x) eps) x) eps))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 (fma.f64 (/.f64 (-.f64 (.f64 #s(literal -4/3 binary64) x) (pow.f64 eps #s(literal -1 binary64))) eps) #s(literal -1 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -4/3 binary64) x (neg.f64 (/.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))) eps) #s(literal -1 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (/ (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x)))) (neg.f64 (/.f64 (-.f64 (.f64 (neg.f64 (cos.f64 x)) (sin.f64 (-.f64 x (neg.f64 eps)))) (neg.f64 (.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))) (*.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))))
#s(approx (* (+ (* -1/6 (* eps eps)) 1) eps) (neg.f64 (*.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal -2 binary64))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (* (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (neg (cos x))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (-.f64 x (neg.f64 eps)))))
#s(approx (- (* (cos eps) (cos x)) (* (sin eps) (sin x))) (cos.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval93.0ms (1.3%)

Memory: 21.4MiB live, 113.5MiB allocated; 7ms collecting garbage
Compiler: Compiled 62 457 to 2 559 computations (95.9% saved)

prune132.0ms (1.8%)

Memory

-27.9MiB live, 82.4MiB allocated; 131ms collecting garbage

Pruning

30 alts after pruning (24 fresh and 6 done)

	Pruned	Kept	Total
New	495	12	507
Fresh	1	12	13
Picked	3	2	5
Done	1	4	5
Total	500	30	530

Accuracy

100.0%

Counts

530 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.2%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 (+.f64 eps (PI.f64)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	99.9%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x (PI.f64)) (+.f64 x eps))) (cos.f64 (-.f64 (+.f64 x (PI.f64)) (+.f64 x eps)))) #s(literal 2 binary64)))
	100.0%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (neg.f64 (cos.f64 x))))
	99.9%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (-.f64 (.f64 #s(approx (cos eps) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))) (neg.f64 (cos.f64 x))))
	99.9%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
✓	99.7%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	99.2%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
	98.8%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
	99.2%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
	98.4%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
	99.8%	(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
	62.0%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	61.9%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	7.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
	7.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓	61.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
	98.4%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) eps))))
	98.4%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps eps))))))))
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✓	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) eps))))
	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
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	98.9%	#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) eps eps)))))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
✓	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))

Compiler

Compiled 7 061 to 1 499 computations (78.8% saved)

regimes47.0ms (0.6%)

Memory

6.6MiB live, 100.8MiB allocated; 8ms collecting garbage

Counts

55 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (+ ( x x) 1) (*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
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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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) 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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
(-.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)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))) #s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 4/3 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (tan.f64 (+.f64 x 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 #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 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 (+.f64 eps (PI.f64)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x (PI.f64)) (+.f64 x eps))) (cos.f64 (-.f64 (+.f64 x (PI.f64)) (+.f64 x eps)))) #s(literal 2 binary64)))
(-.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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (-.f64 (.f64 #s(approx (cos eps) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (neg.f64 (cos.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 (fma.f64 eps (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(/.f64 (-.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 (-.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 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64)) (.f64 #s(literal 1 binary64) (/.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 (fma.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 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #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)))) (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (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)))) #s(literal 1/6 binary64))) eps (.f64 #s(literal 1 binary64) (/.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

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

Calls

3 calls:

15.0ms	x
15.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes42.0ms (0.6%)

Memory

-4.2MiB live, 91.9MiB allocated; 7ms collecting garbage

Counts

49 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	x
11.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.5%)

Memory

-5.6MiB live, 88.0MiB allocated; 4ms collecting garbage

Counts

48 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (+ ( x x) 1) (*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) 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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
(-.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)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))) #s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 4/3 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (tan.f64 (+.f64 x 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 #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 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 (+.f64 eps (PI.f64)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x (PI.f64)) (+.f64 x eps))) (cos.f64 (-.f64 (+.f64 x (PI.f64)) (+.f64 x eps)))) #s(literal 2 binary64)))
(-.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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (.f64 (-.f64 (.f64 #s(approx (cos eps) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x))) (neg.f64 (cos.f64 x))))

Outputs

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

Calls

3 calls:

13.0ms	x
11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.5%)

Memory

39.7MiB live, 86.5MiB allocated; 2ms collecting garbage

Counts

45 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (+ ( x x) 1) (*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) 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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
(-.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)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))) #s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 4/3 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (tan.f64 (+.f64 x 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 #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 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 (+.f64 eps (PI.f64)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.5%)

Memory

-23.9MiB live, 72.3MiB allocated; 4ms collecting garbage

Counts

42 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (+ ( x x) 1) (*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) 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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
(-.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)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))) #s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 4/3 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (tan.f64 (+.f64 x 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 #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 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) #s(approx (neg (sin eps)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))

Outputs

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

Calls

3 calls:

12.0ms	eps
11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes33.0ms (0.4%)

Memory

26.6MiB live, 73.3MiB allocated; 2ms collecting garbage

Counts

40 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

10.0ms	x
10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.5%)

Memory

-25.6MiB live, 70.9MiB allocated; 4ms collecting garbage

Counts

39 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (+ ( x x) 1) (*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) 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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
(-.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)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))) #s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 4/3 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (tan.f64 (+.f64 x 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 #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 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
#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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))

Outputs

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

Calls

3 calls:

11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	eps
9.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes30.0ms (0.4%)

Memory

18.7MiB live, 65.5MiB allocated; 1ms collecting garbage

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (+ ( x x) 1) (*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) 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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
(-.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)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))) #s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 4/3 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (tan.f64 (+.f64 x 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 #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 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) eps))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))

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

Calls

3 calls:

10.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.4%)

Memory

-28.0MiB live, 66.0MiB allocated; 3ms collecting garbage

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 #s(approx (+ ( x x) 1) (*.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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))))) #s(approx (* (+ (* x x) 1) eps) (fma.f64 (*.f64 x x) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 x x #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (- (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (+.f64 (fma.f64 x x (.f64 x eps)) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 #s(approx (+ (* eps (* x (+ 1 (* 4/3 (* eps eps))))) (* (* eps eps) (+ 1 (* 2/3 (* eps eps))))) (.f64 x eps)) x (.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 x eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (-.f64 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x))))) 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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (.f64 (.f64 eps eps) (.f64 eps 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
(-.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)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* x x)) 2/15) #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)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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))))) #s(approx (* (+ (* (/ x eps) 4/3) 2/3) (pow eps 4)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 4/3 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (*.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) #s(literal -1 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 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 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 4 binary64))))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (neg (cos x)) (-.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(approx (- (* (sin (+ eps x)) (neg (cos x))) (* (cos (+ eps x)) (neg (sin x)))) (neg.f64 #s(approx (sin eps) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)))) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (tan.f64 (+.f64 x 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 #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 #s(approx (+ ( (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #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))))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes30.0ms (0.4%)

Memory

7.0MiB live, 56.7MiB allocated; 9ms collecting garbage

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps
7.0ms	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 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.2%)

Memory

30.1MiB live, 30.1MiB allocated; 0ms collecting garbage

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

4.0ms	eps
4.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	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 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.2%)

Memory

-18.5MiB live, 28.5MiB allocated; 1ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

Calls

3 calls:

4.0ms	eps
3.0ms	x
3.0ms	(-.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 9 to 10 computations (-11.1% saved)

regimes5.0ms (0.1%)

Memory

13.6MiB live, 13.7MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

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

Calls

3 calls:

1.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms	eps
1.0ms	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 9 to 10 computations (-11.1% saved)

regimes5.0ms (0.1%)

Memory

-30.6MiB live, 14.8MiB allocated; 3ms collecting garbage

Accuracy

Total -58.9b remaining (-5715.7%)

Threshold costs -58.9b (-5715.7%)

Counts

2 → 1

Calls

Call 1

Inputs

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))

Calls

3 calls:

3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms	x
1.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations373.0ms (5.1%)

Memory

50.3MiB live, 468.4MiB allocated; 50ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 1 112 to 178 computations (84% saved)

preprocess186.0ms (2.5%)

Memory: 30.5MiB live, 236.7MiB allocated; 96ms collecting garbage
Compiler: Compiled 2 308 to 416 computations (82% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze61.0ms (0.8%)

sample4.2s (57.3%)

explain87.0ms (1.2%)

preprocess54.0ms (0.7%)

series12.0ms (0.2%)

rewrite195.0ms (2.6%)

eval9.0ms (0.1%)

prune25.0ms (0.3%)

series163.0ms (2.2%)

rewrite248.0ms (3.4%)

eval226.0ms (3.1%)

prune30.0ms (0.4%)

series137.0ms (1.9%)

rewrite275.0ms (3.7%)

eval85.0ms (1.2%)

prune28.0ms (0.4%)

series102.0ms (1.4%)

rewrite238.0ms (3.2%)

eval93.0ms (1.3%)

prune132.0ms (1.8%)

regimes47.0ms (0.6%)

regimes42.0ms (0.6%)

regimes40.0ms (0.5%)

regimes36.0ms (0.5%)

regimes36.0ms (0.5%)

regimes33.0ms (0.4%)

regimes34.0ms (0.5%)

regimes30.0ms (0.4%)

regimes31.0ms (0.4%)

regimes30.0ms (0.4%)

regimes13.0ms (0.2%)

regimes12.0ms (0.2%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

derivations373.0ms (5.1%)

preprocess186.0ms (2.5%)

end0.0ms (0%)

Profiling