Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze50.0ms (0.3%)

Memory

22.9MiB live, 60.4MiB allocated

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)

sample7.8s (51.9%)

Memory

-116.9MiB live, 7 169.8MiB allocated

Samples

4.3s	25 800×	0	invalid
785.0ms	5 603×	0	valid
607.0ms	2 653×	1	valid

Precisions

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

ival-tan: 947.0ms (24.8% of total)

const: 664.0ms (17.4% of total)

ival-<=: 480.0ms (12.6% of total)

ival-add: 367.0ms (9.6% of total)

ival-fabs: 367.0ms (9.6% of total)

ival-mult: 323.0ms (8.5% of total)

ival-sub: 213.0ms (5.6% of total)

ival-<: 199.0ms (5.2% of total)

ival-and: 115.0ms (3% of total)

adjust: 79.0ms (2.1% of total)

exact: 51.0ms (1.3% of total)

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

Bogosity

explain103.0ms (0.7%)

Memory

-24.7MiB live, 214.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
224	1	(-1.3406066100833134e-152 2.938703641824957e-155)	8	(2.2492287058178203e-167 2.814634858253697e-169)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
2	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	217	13
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	216	8
-	1	31

Precision

0.9953917050691244

Recall

0.9642857142857143

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	216	8	0
-	1	5	26

Precision?

0.9739130434782609

Recall?

1.0

Freqs

test

number	freq
0	39
1	215
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

17.010986328125

Average Time

0.06644916534423828

Samples

10.0ms	87×	1	valid
8.0ms	168×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 63 to 26 computations (58.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-tan: 6.0ms (50.9% of total)

adjust: 2.0ms (17% of total)

ival-add: 2.0ms (17% of total)

ival-sub: 2.0ms (17% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess22.0ms (0.1%)

Memory

34.4MiB live, 34.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify25.0ms (0.2%)

Memory

-33.1MiB live, 5.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tan.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

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

localize24.0ms (0.2%)

Memory

26.0MiB live, 26.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.10034366450427552	(tan.f64 (+.f64 x eps))
accuracy	23.576629590460417	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

9.0ms	87×	1	valid
8.0ms	168×	0	valid
0.0ms	1×	3	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-tan: 5.0ms (48.4% of total)

adjust: 2.0ms (19.4% of total)

ival-add: 2.0ms (19.4% of total)

ival-sub: 2.0ms (19.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

4 → 31

Calls

Call 1

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

Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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)))
(+ (* 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)))
eps
(+ eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* 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)))
(+ (* 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)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify194.0ms (1.3%)

Memory

-13.5MiB live, 99.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	950
1	464	884
2	1535	873
3	5933	841
0	8521	794

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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)))
(+ (* 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)))
eps
(+ eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* 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)))
(+ (* 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)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

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

rewrite256.0ms (1.7%)

Memory

-1.7MiB live, 117.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16

Stop Event

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

Counts

4 → 259

Calls

Call 1

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

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

eval37.0ms (0.2%)

Memory: 3.0MiB live, 40.3MiB allocated
Compiler: Compiled 7 782 to 1 013 computations (87% saved)

prune16.0ms (0.1%)

Memory

24.7MiB live, 24.8MiB allocated

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	264	16	280
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	264	17	281

Accuracy

100.0%

Counts

281 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.2%	(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
	63.0%	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
	63.2%	(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
▶	63.0%	(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
	63.0%	(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	63.0%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
▶	63.2%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
	63.0%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	63.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
▶	63.2%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
✓	63.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	23.7%	(-.f64 (tan.f64 (+.f64 x eps)) (exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 1 001 to 480 computations (52% saved)

simplify338.0ms (2.2%)

Memory

-7.8MiB live, 146.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (tan.f64 eps) (tan.f64 x))
cost-diff	0	(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
cost-diff	256	(-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
cost-diff	19712	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
cost-diff	0	(tan.f64 eps)
cost-diff	0	(+.f64 (tan.f64 eps) (tan.f64 x))
cost-diff	0	(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
cost-diff	0	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
cost-diff	0	(neg.f64 (cos.f64 x))
cost-diff	0	(sin.f64 x)
cost-diff	192	(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
cost-diff	5888	(pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (cos.f64 eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	26816	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
cost-diff	79872	(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	1230
0	115	1230
1	192	1088
2	450	1055
3	1641	912
0	8317	891

Stop Event

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

Calls

Call 1

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

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

localize391.0ms (2.6%)

Memory

3.8MiB live, 317.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy	0.0078125	(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
accuracy	0.03125	(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
accuracy	23.547449004099445	(-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
accuracy	0	(tan.f64 eps)
accuracy	0	(neg.f64 (tan.f64 eps))
accuracy	0.0078125	(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy	23.576629590460417	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))
accuracy	0.10034366450427552	(tan.f64 (+.f64 eps x))
accuracy	23.560590085209938	(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
accuracy	0	(sin.f64 eps)
accuracy	0	(cos.f64 eps)
accuracy	0.01171875	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	0.8403186591993302	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.015625	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.14453125	(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.3515625	(*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
accuracy	0.984375	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

159.0ms	89×	1	valid
91.0ms	163×	0	valid
80.0ms	4×	3	valid

Compiler

Compiled 2 372 to 131 computations (94.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 294.0ms

ival-mult: 84.0ms (28.6% of total)

ival-div: 50.0ms (17% of total)

ival-cos: 36.0ms (12.2% of total)

ival-add: 25.0ms (8.5% of total)

ival-tan: 21.0ms (7.1% of total)

ival-pow: 20.0ms (6.8% of total)

adjust: 16.0ms (5.4% of total)

const: 12.0ms (4.1% of total)

ival-sub: 11.0ms (3.7% of total)

ival-pow2: 7.0ms (2.4% of total)

ival-sin: 6.0ms (2% of total)

ival-neg: 5.0ms (1.7% of total)

exact: 1.0ms (0.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series113.0ms (0.7%)

Memory

-11.2MiB live, 130.6MiB allocated

Counts

26 → 148

Calls

Call 1

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

Outputs
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))
-1/2
(- (* -1/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
-1
(- (* -1/2 (pow x 2)) 1)
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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)))
(+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (* -1/2 (/ (sin eps) (cos eps))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* 1/24 (/ (sin eps) (cos eps))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (+ (* 1/24 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* -1/720 (/ (sin eps) (cos eps))) (+ (* -2/15 (/ (sin eps) (cos eps))) (+ (* -1/120 (/ (sin eps) (cos eps))) (* 1/18 (/ (sin eps) (cos eps)))))))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* -1/2 (/ (* x (sin eps)) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/6 x))))) (/ (sin eps) (cos eps)))
(* 1/3 x)
(* x (+ 1/3 (* 4/9 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* 17/45 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2))))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 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)))))))))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ (* 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)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* x (+ 1 (* -1 (/ (* x (sin eps)) (cos eps)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/6 x)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* x (- (* x (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))) 1/6))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ -1 (cos x))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x))))
(sin x)
(* -1 (cos x))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (cos x) 2)
(/ (sin (+ eps x)) (cos (+ eps x)))
(cos x)
(* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* 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)))
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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)))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x))))))
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (cos x)))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* 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)))
(* -1 eps)
(* eps (- (* -1/3 (pow eps 2)) 1))
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))
(+ (sin x) (* -1 (/ (* eps (pow (sin x) 2)) (cos x))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* -1/3 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (pow (sin x) 2) (cos x))) (* -2/15 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(sin eps)
(cos eps)
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
46.0ms	x	@	-inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 2) (tan (+ eps x)) (cos x) (neg (tan eps)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
22.0ms	x	@	inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 2) (tan (+ eps x)) (cos x) (neg (tan eps)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
12.0ms	eps	@	inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 2) (tan (+ eps x)) (cos x) (neg (tan eps)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
10.0ms	eps	@	-inf	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 2) (tan (+ eps x)) (cos x) (neg (tan eps)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))
10.0ms	eps	@	0	((+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (pow (neg (cos x)) -1) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (sin x) (neg (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 2) (tan (+ eps x)) (cos x) (neg (tan eps)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x)))

simplify173.0ms (1.2%)

Memory

26.1MiB live, 217.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	750	4894
1	2388	4594
0	8057	4351

Stop Event

1×	iter limit
1×	node limit

Counts

148 → 146

Calls

Call 1

Inputs
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))
-1/2
(- (* -1/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
-1
(- (* -1/2 (pow x 2)) 1)
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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)))
(+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (* -1/2 (/ (sin eps) (cos eps))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* 1/24 (/ (sin eps) (cos eps))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (+ (* 1/24 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* -1/720 (/ (sin eps) (cos eps))) (+ (* -2/15 (/ (sin eps) (cos eps))) (+ (* -1/120 (/ (sin eps) (cos eps))) (* 1/18 (/ (sin eps) (cos eps)))))))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* -1/2 (/ (* x (sin eps)) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/6 x))))) (/ (sin eps) (cos eps)))
(* 1/3 x)
(* x (+ 1/3 (* 4/9 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* 17/45 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 17/45 (* 248/945 (pow x 2))))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 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)))))))))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ (* 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)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* x (+ 1 (* -1 (/ (* x (sin eps)) (cos eps)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/6 x)))))
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* x (- (* x (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))) 1/6))))))
(- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ -1 (cos x))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x))))
(sin x)
(* -1 (cos x))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (cos x) 2)
(/ (sin (+ eps x)) (cos (+ eps x)))
(cos x)
(* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* 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)))
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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)))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x))))))
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (cos x)))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* 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)))
(* -1 eps)
(* eps (- (* -1/3 (pow eps 2)) 1))
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))
(+ (sin x) (* -1 (/ (* eps (pow (sin x) 2)) (cos x))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* -1/3 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (pow (sin x) 2) (cos x))) (* -2/15 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))))
(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(sin eps)
(cos eps)
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/3 (* eps x)))
(fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x #s(literal 1/3 binary64))
(+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64))
(+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 eps x) #s(literal 4/3 binary64)) x (.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* -1/3 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(fma.f64 (fma.f64 #s(literal -2/9 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -17/135 binary64) (.f64 x x) #s(literal -2/9 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
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(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) (/.f64 eps (cos.f64 x)))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(+ (sin x) (* eps (cos x)))
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(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x))))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
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(+ (* 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)))
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(* eps (- (* -1/3 (pow eps 2)) 1))
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(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))
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(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))
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(+ (sin x) (* -1 (/ (* eps (pow (sin x) 2)) (cos x))))
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(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (pow (sin x) 2) (cos x))) (* -2/15 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x))))))))
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(* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps)
(* eps (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (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 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) eps)
(sin eps)
(sin.f64 eps)
(cos eps)
(cos.f64 eps)
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (pow.f64 eps #s(literal 3 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 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 (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 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps eps)))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 (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 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps eps)))))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (/ (sin eps) (cos eps)))
(/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps))
(* -1 (* eps (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(*.f64 eps (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (+.f64 (+.f64 (+.f64 (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (+.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (-.f64 (/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) #s(literal 1/3 binary64))) eps)))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))

rewrite240.0ms (1.6%)

Memory

-14.7MiB live, 268.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	657
0	115	611
1	524	453
2	5211	453
0	8318	425

Stop Event

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

Counts

26 → 724

Calls

Call 1

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

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

eval301.0ms (2%)

Memory: 1.4MiB live, 388.6MiB allocated
Compiler: Compiled 137 917 to 6 823 computations (95.1% saved)

prune41.0ms (0.3%)

Memory

0.3MiB live, 87.1MiB allocated

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	1 244	14	1 258
Fresh	4	7	11
Picked	5	0	5
Done	0	1	1
Total	1 253	22	1 275

Accuracy

100.0%

Counts

1 275 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.2%	(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
▶	63.0%	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
	63.0%	(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x)))
▶	63.0%	(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	63.0%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	63.0%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	100.0%	(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) (.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
	99.7%	(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
▶	63.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
	63.2%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/3 binary64) #s(literal -1 binary64)) eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	63.2%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
✓	63.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	23.7%	(-.f64 (tan.f64 (+.f64 x eps)) (exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))))
	100.0%	#s(approx (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (*.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps))
	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
▶	5.6%	#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))

Compiler

Compiled 2 659 to 1 084 computations (59.2% saved)

simplify165.0ms (1.1%)

Memory

3.3MiB live, 195.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(+.f64 eps x)
cost-diff	0	(sin.f64 (+.f64 eps x))
cost-diff	0	(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
cost-diff	0	(+.f64 eps x)
cost-diff	0	(cos.f64 (+.f64 eps x))
cost-diff	0	(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
cost-diff	6080	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
cost-diff	0	(tan.f64 (+.f64 eps x))
cost-diff	0	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
cost-diff	0	(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
cost-diff	0	#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
cost-diff	6464	(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
cost-diff	12608	(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	26752	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	1085
0	147	1075
1	241	948
2	530	919
3	1845	816
0	8529	787

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 1/3 binary64)
(fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
eps
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(/.f64 (sin.f64 x) (cos.f64 x))
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(literal 0 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
#s(literal -1 binary64)
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(literal -1 binary64)
(sin.f64 (+.f64 eps x))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(cos.f64 x)
(*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))
(cos.f64 (+.f64 eps x))
(neg.f64 (sin.f64 x))
(sin.f64 x)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)))))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps)
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)))))) eps eps)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) eps (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 1/3 binary64)
(fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
eps
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(/.f64 (sin.f64 x) (cos.f64 x))
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(literal 0 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
#s(literal 1 binary64)
(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
#s(literal -1 binary64)
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(literal -1 binary64)
(sin.f64 (+.f64 eps x))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)))) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(cos.f64 x)
(*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))
(*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(neg.f64 (sin.f64 x))
(sin.f64 x)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

localize356.0ms (2.4%)

Memory

18.7MiB live, 301.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.07979192021901796	(cos.f64 (+.f64 eps x))
accuracy	0.09185504389405152	(sin.f64 (+.f64 eps x))
accuracy	23.556539786911024	(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
accuracy	0	(neg.f64 (tan.f64 x))
accuracy	0.07979192021901796	(cos.f64 (+.f64 eps x))
accuracy	0.09185504389405152	(sin.f64 (+.f64 eps x))
accuracy	23.588557184306136	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
accuracy	0.01171875	(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
accuracy	0.10034366450427552	(tan.f64 (+.f64 eps x))
accuracy	0.19921875	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
accuracy	23.576629590460417	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
accuracy	60.406863343117074	#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
accuracy	0.021816259768442016	(pow.f64 (cos.f64 x) #s(literal 4 binary64))
accuracy	0.0234375	(pow.f64 (cos.f64 x) #s(literal 3 binary64))
accuracy	0.05636895527994348	#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
accuracy	0.14453125	(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

Samples

137.0ms	89×	1	valid
136.0ms	163×	0	valid
11.0ms	4×	3	valid

Compiler

Compiled 1 844 to 182 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 231.0ms

ival-add: 58.0ms (25.2% of total)

ival-mult: 45.0ms (19.5% of total)

ival-pow: 32.0ms (13.9% of total)

ival-div: 22.0ms (9.5% of total)

adjust: 20.0ms (8.7% of total)

const: 14.0ms (6.1% of total)

ival-tan: 9.0ms (3.9% of total)

ival-sin: 7.0ms (3% of total)

ival-pow2: 7.0ms (3% of total)

ival-sub: 6.0ms (2.6% of total)

ival-cos: 5.0ms (2.2% of total)

ival-neg: 4.0ms (1.7% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series53.0ms (0.4%)

Memory

-3.6MiB live, 68.0MiB allocated

Counts

21 → 148

Calls

Call 1

Inputs
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
(sin.f64 (+.f64 eps x))
(cos.f64 x)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.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 3 binary64))
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
(neg.f64 (tan.f64 x))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

Outputs
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(pow x 3)
(* (pow x 3) (+ 1 (pow x 2)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
(/ (cos eps) (sin eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* -1 (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))) (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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)))
(+ (* 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)))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
(sin eps)
(+ (sin eps) (* x (+ (cos eps) (* -1 (cos eps)))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps))))))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 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)))))))))))
(+ 1 (* -3/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 7/8 (pow x 2)) 3/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))
(+ 1 (* -2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/3 (pow x 2)) 2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/3 (* -34/45 (pow x 2)))) 2)))
(* -1 x)
(* x (- (* -1/3 (pow x 2)) 1))
(* x (- (* (pow x 2) (- (* -2/15 (pow x 2)) 1/3)) 1))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/315 (pow x 2)) 2/15)) 1/3)) 1))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 3) (pow (cos x) 3))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x))))
(sin (+ eps x))
(cos x)
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (cos x) 3)
(pow (cos x) 4)
(* -1 (/ (sin x) (cos x)))
(* (cos x) (cos (+ eps x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x)))))
(sin (- eps (* -1 x)))
(* (cos x) (cos (- eps (* -1 x))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(/ 1 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(/ (+ (* -1 (/ (* eps (sin x)) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ 1 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)
(/ (+ (* eps (- (* -1 (* eps (+ (* -1 (/ (+ 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)))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (/ (sin x) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ 1 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)
(/ (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (sin x) (+ (* -1 (/ (+ 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)))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (cos x))) (+ (* -1 (/ (+ (* -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)))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (/ (* (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) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))))))) (+ (* -1 (/ (+ 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)))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (/ (sin x) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ 1 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* 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)))
(+ (* 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)))
(/ 1 (cos x))
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))))
(* eps (+ 1 (/ x eps)))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(/ 1 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps)))))
(sin (- x (* -1 eps)))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* (cos x) (cos (- x (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)) (- (tan (+ x eps)) (tan x)) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin (+ eps x)) (cos x) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 3) (pow (cos x) 4) (neg (tan x)) (* (cos (+ eps x)) (cos x)))
9.0ms	x	@	0	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)) (- (tan (+ x eps)) (tan x)) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin (+ eps x)) (cos x) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 3) (pow (cos x) 4) (neg (tan x)) (* (cos (+ eps x)) (cos x)))
9.0ms	eps	@	0	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)) (- (tan (+ x eps)) (tan x)) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin (+ eps x)) (cos x) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 3) (pow (cos x) 4) (neg (tan x)) (* (cos (+ eps x)) (cos x)))
9.0ms	x	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)) (- (tan (+ x eps)) (tan x)) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin (+ eps x)) (cos x) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 3) (pow (cos x) 4) (neg (tan x)) (* (cos (+ eps x)) (cos x)))
5.0ms	eps	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)) (- (tan (+ x eps)) (tan x)) (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin (+ eps x)) (cos x) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (cos x) 3) (pow (cos x) 4) (neg (tan x)) (* (cos (+ eps x)) (cos x)))

simplify373.0ms (2.5%)

Memory

1.3MiB live, 156.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	682	4578
1	2182	4084
2	7715	4058
0	8656	3845

Stop Event

1×	iter limit
1×	node limit

Counts

148 → 146

Calls

Call 1

Inputs
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(pow x 3)
(* (pow x 3) (+ 1 (pow x 2)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
(/ (cos eps) (sin eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* -1 (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))) (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* 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)))
(+ (* 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)))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
(sin eps)
(+ (sin eps) (* x (+ (cos eps) (* -1 (cos eps)))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps))))))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 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)))))))))))
(+ 1 (* -3/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 7/8 (pow x 2)) 3/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))
(+ 1 (* -2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 5/3 (pow x 2)) 2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/3 (* -34/45 (pow x 2)))) 2)))
(* -1 x)
(* x (- (* -1/3 (pow x 2)) 1))
(* x (- (* (pow x 2) (- (* -2/15 (pow x 2)) 1/3)) 1))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/315 (pow x 2)) 2/15)) 1/3)) 1))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 3) (pow (cos x) 3))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x))))
(sin (+ eps x))
(cos x)
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (cos x) 3)
(pow (cos x) 4)
(* -1 (/ (sin x) (cos x)))
(* (cos x) (cos (+ eps x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x)))))
(sin (- eps (* -1 x)))
(* (cos x) (cos (- eps (* -1 x))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* 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))))
(/ 1 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(/ (+ (* -1 (/ (* eps (sin x)) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ 1 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)
(/ (+ (* eps (- (* -1 (* eps (+ (* -1 (/ (+ 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)))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (/ (sin x) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ 1 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)
(/ (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (sin x) (+ (* -1 (/ (+ 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)))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (cos x))) (+ (* -1 (/ (+ (* -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)))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (/ (* (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) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))))))) (+ (* -1 (/ (+ 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)))))) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2))) (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (/ (sin x) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ 1 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* 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)))
(+ (* 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)))
(/ 1 (cos x))
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))))
(* eps (+ 1 (/ x eps)))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(/ 1 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps)))))
(sin (- x (* -1 eps)))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* (cos x) (cos (- x (* -1 eps))))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (+ 1 (pow x 2)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 11/15 binary64) (.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 88/189 binary64) (.f64 x x) #s(literal 11/15 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* 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)))
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (-.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (cos eps) (sin eps))
(/.f64 (cos.f64 eps) (sin.f64 eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(-.f64 (/.f64 (cos.f64 eps) (sin.f64 eps)) x)
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) 1)) (/ (cos eps) (sin eps)))
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(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (neg.f64 (cos.f64 x)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 x)))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (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))
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))
#s(literal 0 binary64)
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x))))
(+.f64 #s(literal 0 binary64) eps)
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(fma.f64 (fma.f64 #s(literal 0 binary64) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (neg.f64 eps) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (/.f64 (sin.f64 x) eps) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 eps eps))
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (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 1/3 binary64) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 (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 1/3 binary64) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (+.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps eps)) (/.f64 #s(literal 1/3 binary64) eps)) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (*.f64 eps eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 (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 1/3 binary64) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (+.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps eps)) (/.f64 #s(literal 1/3 binary64) eps)) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (*.f64 eps eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(.f64 (.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps) #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps) eps)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ 1 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (- x (* -1 eps))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps)
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps)))))
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (cos.f64 x)) (sin.f64 x) (/.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (cos.f64 x)) (sin.f64 x) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps) #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps)))))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

rewrite280.0ms (1.9%)

Memory

-33.0MiB live, 220.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	652
0	145	622
1	677	416
2	6528	416
0	8040	388

Stop Event

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

Counts

21 → 489

Calls

Call 1

Inputs
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))
(sin.f64 (+.f64 eps x))
(cos.f64 x)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.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 3 binary64))
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
(neg.f64 (tan.f64 x))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

Outputs
(.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))))))
(.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (*.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))))
(/.f64 (-.f64 (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 1/9 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))))
(/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (tan.f64 x) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 1/3 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) #s(literal 2 binary64))))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 1/3 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) (-.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) (-.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (-.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (-.f64 (.f64 (tan.f64 x) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 1/3 binary64)) (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (*.f64 (tan.f64 x) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(+.f64 eps x)
(+.f64 x eps)
(.f64 (.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 (+.f64 eps x) x))))
(.f64 (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (-.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (pow.f64 (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (neg.f64 (*.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x)))) (neg.f64 (sin.f64 (+.f64 (+.f64 eps x) x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (-.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 2 binary64)))))
(/.f64 (*.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (sin.f64 (+.f64 (+.f64 eps x) x)))
(/.f64 (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) (neg.f64 (sin.f64 x))) (cos.f64 (+.f64 eps x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (-.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (+.f64 (+.f64 eps x) x)) (*.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (-.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 3 binary64)))))
(fma.f64 (.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 x) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (sin.f64 x) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) (sin.f64 #s(literal 0 binary64))))
(fma.f64 (+.f64 (sin.f64 (+.f64 (+.f64 eps x) x)) (sin.f64 (+.f64 eps #s(literal 0 binary64)))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))))
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (neg.f64 x)) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (neg.f64 x))))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))))
(fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 #s(literal -1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))))
(fma.f64 (sin.f64 x) (cos.f64 (-.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (-.f64 eps x))))
(sin.f64 (+.f64 eps #s(literal 0 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (+.f64 (+.f64 eps x) x))) (/.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (sin.f64 (+.f64 (+.f64 eps x) x))))
(-.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)))
(+.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (neg.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (neg.f64 x))))
(+.f64 (.f64 (sin.f64 eps) #s(literal 1 binary64)) (.f64 (cos.f64 eps) (sin.f64 #s(literal 0 binary64))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 (-.f64 eps x))) (.f64 (cos.f64 x) (sin.f64 (-.f64 eps x))))
(+.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x))) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))) (sin.f64 (-.f64 eps x)))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x)))
(sin.f64 (+.f64 eps x))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.f64 x)
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (cos.f64 x))
(*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 3/2 binary64))
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 3 binary64)))
(.f64 (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 3/2 binary64)) (cos.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (cos.f64 x))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 4 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
(exp.f64 (fma.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64) (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 4 binary64)))
(.f64 (.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1/2 binary64))) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (tan.f64 x) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x))
(*.f64 #s(literal -1 binary64) (tan.f64 x))
(*.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x))) (neg.f64 (cos.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (neg.f64 (cos.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))
(neg.f64 (tan.f64 x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
(+.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 x)))
(*.f64 (+.f64 (cos.f64 (+.f64 eps #s(literal 0 binary64))) (cos.f64 (+.f64 (+.f64 eps x) x))) #s(literal 1/2 binary64))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps #s(literal 0 binary64))) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal -2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps #s(literal 0 binary64))) (cos.f64 (+.f64 (+.f64 eps x) x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 eps #s(literal 0 binary64))) (cos.f64 (+.f64 (+.f64 eps x) x)))))

eval145.0ms (1%)

Memory: 33.8MiB live, 193.3MiB allocated
Compiler: Compiled 71 549 to 3 492 computations (95.1% saved)

prune31.0ms (0.2%)

Memory

-9.6MiB live, 64.3MiB allocated

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	736	7	743
Fresh	12	4	16
Picked	4	1	5
Done	0	1	1
Total	752	13	765

Accuracy

100.0%

Counts

765 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.6%	(/.f64 (.f64 (.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 (+.f64 eps x) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	100.0%	(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) (.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
	99.7%	(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
	99.9%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	99.7%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	99.9%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	63.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
▶	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
▶	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
✓	5.6%	#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))

Compiler

Compiled 2 202 to 803 computations (63.5% saved)

simplify264.0ms (1.8%)

Memory

2.6MiB live, 274.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 (+.f64 eps x))
cost-diff	0	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))
cost-diff	0	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps))
cost-diff	0	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
cost-diff	0	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	6400	(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
cost-diff	6592	(fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	2141
0	136	2113
1	264	1839
2	768	1795
3	3013	1481
4	6815	1481
0	8677	1419

Stop Event

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

Calls

Call 1

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

Outputs
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#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
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eps
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(pow.f64 (tan.f64 x) #s(literal 2 binary64))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
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eps
#s(literal 1/3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))))
#s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
eps
#s(literal 4/3 binary64)
#s(literal 1 binary64)
x
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps))
#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)

localize400.0ms (2.7%)

Memory

-23.7MiB live, 361.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))
accuracy	0.00390625	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.07979192021901796	(cos.f64 (+.f64 eps x))
accuracy	0.00390625	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.07979192021901796	(cos.f64 (+.f64 eps x))
accuracy	0.1456338846718458	#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps))
accuracy	0.05636895527994348	#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))))
accuracy	0.109375	(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
accuracy	0.19921875	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	0.8818576432889227	#s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
accuracy	0	(*.f64 eps eps)
accuracy	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
accuracy	0.19921875	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	27.986228113583543	#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
accuracy	0.01171875	(pow.f64 (tan.f64 x) #s(literal 2 binary64))
accuracy	0.015625	(pow.f64 (tan.f64 x) #s(literal 3 binary64))
accuracy	0.05636895527994348	#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
accuracy	0.14453125	(fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))

Samples

175.0ms	87×	1	valid
127.0ms	167×	0	valid
6.0ms	2×	3	valid

Compiler

Compiled 3 447 to 199 computations (94.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 269.0ms

ival-add: 83.0ms (30.8% of total)

ival-mult: 47.0ms (17.5% of total)

ival-sin: 28.0ms (10.4% of total)

ival-pow: 25.0ms (9.3% of total)

adjust: 21.0ms (7.8% of total)

ival-div: 20.0ms (7.4% of total)

const: 17.0ms (6.3% of total)

ival-pow2: 10.0ms (3.7% of total)

ival-tan: 6.0ms (2.2% of total)

ival-sub: 5.0ms (1.9% of total)

ival-cos: 5.0ms (1.9% of total)

ival-neg: 1.0ms (0.4% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series79.0ms (0.5%)

Memory

16.4MiB live, 98.5MiB allocated

Counts

26 → 132

Calls

Call 1

Inputs
(fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))))
#s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
(+.f64 #s(literal 0 binary64) eps)
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))
(sin.f64 eps)
(cos.f64 (+.f64 eps x))
(fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(*.f64 eps eps)
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Outputs
1/3
(+ 1/3 (pow x 4))
(+ 1/3 (* (pow x 4) (+ 1 (* 4/3 (pow x 2)))))
(+ 1/3 (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))))
(* 1/3 eps)
(+ x (* 1/3 eps))
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* 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))))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 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)))))))))))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* x (- (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (sin eps) (* x (+ (cos eps) (* -1 (cos eps)))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps))))))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(pow x 3)
(* (pow x 3) (+ 1 (pow x 2)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(+ 1/3 (/ (pow (sin x) 4) (pow (cos x) 4)))
(+ (* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x))))
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x))))
(* (cos x) (cos (+ eps x)))
(cos (+ eps x))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 2) (pow (cos x) 2))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x)))))
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
eps
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x))))
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(pow eps 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* -1 (* eps (+ (* -1 (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps)))))
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps)))))
(* (cos x) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	x	@	0	((+ (* (tan x) (pow (tan x) 3)) 1/3) (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 0 eps) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x)) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin eps) (cos (+ eps x)) (+ (* (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) eps) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (tan x) 3) (pow (tan x) 2) (* eps eps) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))))
11.0ms	x	@	inf	((+ (* (tan x) (pow (tan x) 3)) 1/3) (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 0 eps) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x)) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin eps) (cos (+ eps x)) (+ (* (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) eps) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (tan x) 3) (pow (tan x) 2) (* eps eps) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))))
11.0ms	x	@	-inf	((+ (* (tan x) (pow (tan x) 3)) 1/3) (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 0 eps) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x)) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin eps) (cos (+ eps x)) (+ (* (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) eps) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (tan x) 3) (pow (tan x) 2) (* eps eps) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))))
8.0ms	eps	@	inf	((+ (* (tan x) (pow (tan x) 3)) 1/3) (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 0 eps) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x)) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin eps) (cos (+ eps x)) (+ (* (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) eps) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (tan x) 3) (pow (tan x) 2) (* eps eps) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))))
8.0ms	eps	@	-inf	((+ (* (tan x) (pow (tan x) 3)) 1/3) (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 0 eps) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x)) (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin eps) (cos (+ eps x)) (+ (* (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) eps) (pow (tan x) 2)) (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (tan x) 3) (pow (tan x) 2) (* eps eps) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (/ (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (* (cos (+ eps x)) (cos x))))

simplify196.0ms (1.3%)

Memory

-16.4MiB live, 169.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	675	5061
1	2332	4384
0	8348	4153

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 131

Calls

Call 1

Inputs
1/3
(+ 1/3 (pow x 4))
(+ 1/3 (* (pow x 4) (+ 1 (* 4/3 (pow x 2)))))
(+ 1/3 (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))))
(* 1/3 eps)
(+ x (* 1/3 eps))
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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)))
(+ (* 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)))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* 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))))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 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)))))))))))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* x (- (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(+ (sin eps) (* x (+ (cos eps) (* -1 (cos eps)))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps))))))))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(pow x 3)
(* (pow x 3) (+ 1 (pow x 2)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(+ 1/3 (/ (pow (sin x) 4) (pow (cos x) 4)))
(+ (* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x))))
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x))))
(* (cos x) (cos (+ eps x)))
(cos (+ eps x))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 3) (pow (cos x) 3))
(/ (pow (sin x) 2) (pow (cos x) 2))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x)))))
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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)))))
(* 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)))))
(* 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)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
eps
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x))))
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(pow eps 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* -1 (* eps (+ (* -1 (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps)))))
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps)))))
(* (cos x) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))

Outputs
1/3
#s(literal 1/3 binary64)
(+ 1/3 (pow x 4))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 4) (+ 1 (* 4/3 (pow x 2)))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 6/5 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ x (* 1/3 eps))
(fma.f64 #s(literal 1/3 binary64) eps x)
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x)
(+ (* 1/3 eps) (* x (+ 1 (* x (+ (* 4/3 eps) (* 4/3 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) (+.f64 eps x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/3 binary64) eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* 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)))
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ eps (* 1/3 (pow eps 3)))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(fma.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) eps (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 4/3 binary64) eps) x)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(+ eps (+ (* 1/3 (pow eps 3)) (* 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))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 4/3 binary64) eps)) x)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* 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)))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 eps eps) #s(literal 4/3 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 3 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 eps x)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* x (- (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (-.f64 (/.f64 (.f64 (cos.f64 eps) #s(literal 2/3 binary64)) (cos.f64 eps)) #s(literal 2/3 binary64)) (fma.f64 #s(literal -1 binary64) (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (+ (cos eps) (* -1 (cos eps)))))
(fma.f64 #s(literal 0 binary64) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps))))))))
(fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))))))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x #s(literal 0 binary64)) x (sin.f64 eps))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64) (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (.f64 (cos.f64 eps) #s(literal -1/2 binary64))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (+ 1 (pow x 2)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 11/15 binary64) (.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 88/189 binary64) (.f64 x x) #s(literal 11/15 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(.f64 (.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)) x) x)
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)
(+ 1/3 (/ (pow (sin x) 4) (pow (cos x) 4)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))
(+ (* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* eps (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) #s(literal 1/3 binary64)) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
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(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))
#s(literal 0 binary64)
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x))))
(+.f64 #s(literal 0 binary64) eps)
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(fma.f64 (fma.f64 #s(literal 0 binary64) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (*.f64 (cos.f64 x) (sin.f64 x)) (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (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))
(pow eps 2)
(*.f64 eps eps)
(+ (* eps x) (pow x 2))
(*.f64 x (+.f64 eps x))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))
(* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(*.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) eps)
(* eps (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(*.f64 (+.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps)
(* (pow eps 4) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
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(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(*.f64 (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 1/3 binary64) (fma.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 (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 1/3 binary64) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (+.f64 (/.f64 (/.f64 (/.f64 (sin.f64 x) eps) eps) (cos.f64 x)) (/.f64 #s(literal 1/3 binary64) eps)) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (.f64 eps eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(.f64 (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 1/3 binary64) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) eps)) (/.f64 (/.f64 (/.f64 (sin.f64 x) eps) eps) (cos.f64 x))) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (.f64 eps eps)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 3) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))))
(.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
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(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
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(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))))
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(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4)))))
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(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
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(* (pow eps 2) (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))))
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(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
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(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
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(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
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(* -1 (* eps (+ (* -1 (+ 1/3 (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps)) (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))))
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
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(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ (* 1/3 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (/ (* (sin x) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)))) (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64))) (cos.f64 x)) (/.f64 (+.f64 (-.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (-.f64 (/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) #s(literal 1/3 binary64)) eps)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(.f64 (+.f64 (-.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (-.f64 (/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) #s(literal 1/3 binary64)) (.f64 eps eps))
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps)))))
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(.f64 (+.f64 (-.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (-.f64 (/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps)) #s(literal 1/3 binary64)) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x (-.f64 #s(literal 1/3 binary64) (/.f64 (neg.f64 (fma.f64 x (/.f64 x eps) x)) eps))) (*.f64 eps eps))

rewrite286.0ms (1.9%)

Memory

20.5MiB live, 271.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	2056
0	136	1989
1	781	1402
0	8695	1312

Stop Event

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

Counts

26 → 494

Calls

Call 1

Inputs
(fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps)
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))))
#s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
(+.f64 #s(literal 0 binary64) eps)
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
#s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))
(sin.f64 eps)
(cos.f64 (+.f64 eps x))
(fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
#s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(*.f64 eps eps)
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Outputs
(*.f64 (-.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/3 binary64))))
(.f64 (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1/9 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/3 binary64)))))
(/.f64 (-.f64 #s(literal 1/9 binary64) (pow.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
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(.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x)))
(/.f64 (fma.f64 (pow.f64 (.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/27 binary64) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 2 binary64))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 #s(literal -1/3 binary64) (*.f64 eps eps))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 #s(literal -1/3 binary64) (.f64 eps eps))) (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x)))) (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 3 binary64)) (pow.f64 (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 3 binary64)))))
(fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))
(fma.f64 eps (.f64 eps #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))
(fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))
(fma.f64 x (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))) (/.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 #s(literal -1/3 binary64) (.f64 eps eps)))))
(+.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(+.f64 (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))
(.f64 (/.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(pow.f64 (/.f64 (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) #s(literal -1 binary64))
(/.f64 (.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (neg.f64 (/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (neg.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)))))
(/.f64 (neg.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))))
(neg.f64 (/.f64 (neg.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(neg.f64 (/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))

eval201.0ms (1.3%)

Memory: 4.4MiB live, 266.6MiB allocated
Compiler: Compiled 160 185 to 4 322 computations (97.3% saved)

prune52.0ms (0.3%)

Memory

-19.8MiB live, 107.2MiB allocated

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	791	15	806
Fresh	4	2	6
Picked	4	1	5
Done	0	2	2
Total	799	20	819

Accuracy

100.0%

Counts

819 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.7%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))
	99.8%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
	99.7%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
	99.3%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	100.0%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps 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))) (cos.f64 x)))
	100.0%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
	100.0%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
	99.7%	(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	63.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.9%	(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
	99.7%	(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
✓	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
	99.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
	98.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
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✓	5.6%	#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))

Compiler

Compiled 6 205 to 1 160 computations (81.3% saved)

regimes44.0ms (0.3%)

Memory

34.7MiB live, 71.8MiB allocated

Counts

53 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
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(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
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(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(-.f64 (tan.f64 (+.f64 x eps)) (exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/3 binary64) #s(literal -1 binary64)) eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(/.f64 (.f64 (.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 (+.f64 eps x) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps 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))) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) (.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (*.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes71.0ms (0.5%)

Memory

-18.0MiB live, 70.1MiB allocated

Counts

52 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
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(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) (.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps eps))
#s(approx (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (*.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.3%)

Memory

-12.5MiB live, 62.2MiB allocated

Counts

45 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(-.f64 (tan.f64 (+.f64 x eps)) (exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/3 binary64) #s(literal -1 binary64)) eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(/.f64 (.f64 (.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 (+.f64 eps x) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps 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))) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) #s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.3%)

Memory

23.2MiB live, 64.0MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(-.f64 (tan.f64 (+.f64 x eps)) (exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/3 binary64) #s(literal -1 binary64)) eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(/.f64 (.f64 (.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 (+.f64 eps x) x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
(fma.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Outputs

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

Calls

3 calls:

18.0ms	eps
10.0ms	x
10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes35.0ms (0.2%)

Memory

-19.6MiB live, 55.1MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 eps x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(-.f64 (tan.f64 (+.f64 x eps)) (exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/3 binary64) #s(literal -1 binary64)) eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))

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

Calls

3 calls:

13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms	x
9.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.1%)

Memory

27.2MiB live, 27.2MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))

Outputs

(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.1%)

Memory

-12.8MiB live, 25.0MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))

Outputs

(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))

Calls

3 calls:

5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	x
5.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.3%)

Memory

-16.1MiB live, 24.9MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (neg.f64 #s(approx (+ ( (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))))

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

Calls

3 calls:

29.0ms	x
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.1%)

Memory

17.5MiB live, 48.6MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(approx (+ (* eps (+ (* 4/3 (pow (tan x) 2)) (+ (* (tan x) (pow (tan x) 3)) 1/3))) (+ (tan x) (pow (tan x) 3))) (fma.f64 #s(literal 1/3 binary64) eps x)) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

Calls

3 calls:

11.0ms	eps
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	x

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`eps`
99.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory

-6.7MiB live, 30.9MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Outputs

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

Calls

3 calls:

7.0ms	x
4.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps) eps)))) eps eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

-21.3MiB live, 17.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))

Outputs
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.6%	1	`x`
5.6%	1	`eps`
5.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify43.0ms (0.3%)

Memory

21.2MiB live, 108.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	175	1119
1	202	1119
2	219	1119
3	243	1119
4	275	1119
5	313	1119
6	347	1119
7	380	1119
8	417	1119
9	448	1119
10	457	1119

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps 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))) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal 1/3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps 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))) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 eps)) #s(literal 1/2 binary64)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 #s(literal 1/2 binary64) (+.f64 (cos.f64 eps) (cos.f64 (+.f64 (+.f64 eps x) x)))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) (+.f64 #s(literal 0 binary64) eps)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (+ (* (sin (+ eps x)) (cos x)) (* (cos (+ eps x)) (neg (sin x)))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) x) x #s(literal 1/3 binary64)) eps x) eps (.f64 x x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 eps x))))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (/ (sin x) (cos x))) (* 1/3 (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x)))) eps) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2))))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/3) (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) (+ (/ (pow (sin x) 4) (pow (cos x) 4)) 1/3))) eps) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x)))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 (+.f64 eps x) x)))) eps eps))
#s(approx (+ (* (sin x) (pow (neg (cos x)) -1)) (tan (+ eps x))) #s(literal 0 binary64))

soundness1.5s (9.8%)

Memory

-25.7MiB live, 817.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	2056
0	136	1989
1	781	1402
0	8695	1312
0	682	4578
1	2182	4084
2	7715	4058
0	8656	3845
0	90	652
0	145	622
1	677	416
2	6528	416
0	8040	388
0	750	4894
1	2388	4594
0	8057	4351
0	675	5061
1	2332	4384
0	8348	4153
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	157	950
1	464	884
2	1535	873
3	5933	841
0	8521	794

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 1 412 to 390 computations (72.4% saved)

preprocess131.0ms (0.9%)

Memory: 6.6MiB live, 88.5MiB allocated
Compiler: Compiled 2 270 to 388 computations (82.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

start0.0ms (0%)

analyze50.0ms (0.3%)

sample7.8s (51.9%)

explain103.0ms (0.7%)

preprocess22.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify25.0ms (0.2%)

localize24.0ms (0.2%)

series11.0ms (0.1%)

simplify194.0ms (1.3%)

rewrite256.0ms (1.7%)

eval37.0ms (0.2%)

prune16.0ms (0.1%)

simplify338.0ms (2.2%)

localize391.0ms (2.6%)

series113.0ms (0.7%)

simplify173.0ms (1.2%)

rewrite240.0ms (1.6%)

eval301.0ms (2%)

prune41.0ms (0.3%)

simplify165.0ms (1.1%)

localize356.0ms (2.4%)

series53.0ms (0.4%)

simplify373.0ms (2.5%)

rewrite280.0ms (1.9%)

eval145.0ms (1%)

prune31.0ms (0.2%)

simplify264.0ms (1.8%)

localize400.0ms (2.7%)

series79.0ms (0.5%)

simplify196.0ms (1.3%)

rewrite286.0ms (1.9%)

eval201.0ms (1.3%)

prune52.0ms (0.3%)

regimes44.0ms (0.3%)

regimes71.0ms (0.5%)

regimes41.0ms (0.3%)

regimes41.0ms (0.3%)

regimes35.0ms (0.2%)

regimes20.0ms (0.1%)

regimes21.0ms (0.1%)

regimes41.0ms (0.3%)

regimes22.0ms (0.1%)

regimes17.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

simplify43.0ms (0.3%)

soundness1.5s (9.8%)

preprocess131.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18