Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

analyze44.0ms (0.3%)

Memory

-0.6MiB live, 76.3MiB 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)

sample6.8s (52.1%)

Memory

-80.9MiB live, 6 871.0MiB allocated

Samples

3.8s	26 139×	0	invalid
743.0ms	5 506×	0	valid
684.0ms	2 750×	1	valid

Precisions

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

const: 708.0ms (18.6% of total)

ival-add: 619.0ms (16.3% of total)

ival-tan: 613.0ms (16.1% of total)

ival-<=: 464.0ms (12.2% of total)

ival-mult: 424.0ms (11.2% of total)

ival-sub: 245.0ms (6.4% of total)

ival-<: 240.0ms (6.3% of total)

ival-fabs: 233.0ms (6.1% of total)

ival-and: 99.0ms (2.6% of total)

adjust: 96.0ms (2.5% of total)

exact: 46.0ms (1.2% of total)

ival-assert: 12.0ms (0.3% of total)

Bogosity

explain175.0ms (1.4%)

Memory

-35.5MiB live, 155.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
222	2	(4.9684126565015066e-220 4.500062827463338e-223)	3	(-2.7047159038723304e-190 5.820920694496905e-192)	`(-.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	221	9
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	220	3
-	2	31

Precision

0.990990990990991

Recall

0.9865470852017937

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	220	3	0
-	2	5	26

Precision?

0.9695652173913043

Recall?

1.0

Freqs

test

number	freq
0	34
1	221
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms	196×	1	valid
16.0ms	312×	0	valid
1.0ms	4×	2	valid

Compiler

Compiled 83 to 34 computations (59% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-tan: 10.0ms (46.2% of total)

adjust: 4.0ms (18.5% of total)

ival-add: 3.0ms (13.9% of total)

ival-sub: 3.0ms (13.9% of total)

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

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

preprocess25.0ms (0.2%)

Memory

-11.2MiB live, 25.0MiB 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
▶	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

4.6MiB live, 4.6MiB 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)

localize55.0ms (0.4%)

Memory

-21.4MiB live, 25.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.08056588607446653	(tan.f64 (+.f64 x eps))
accuracy	25.26552661617361	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

10.0ms	98×	1	valid
7.0ms	156×	0	valid
0.0ms	2×	2	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 (49.3% of total)

adjust: 2.0ms (19.7% of total)

ival-add: 2.0ms (19.7% of total)

ival-sub: 2.0ms (19.7% of total)

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

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

series11.0ms (0.1%)

Memory

11.3MiB live, 11.4MiB 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))

simplify162.0ms (1.2%)

Memory

19.0MiB live, 248.2MiB 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)

rewrite146.0ms (1.1%)

Memory

18.9MiB live, 211.5MiB 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)))
(*.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 (+.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)))
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(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)))

eval78.0ms (0.6%)

Memory: -41.7MiB live, 91.2MiB allocated
Compiler: Compiled 7 782 to 1 013 computations (87% saved)

prune12.0ms (0.1%)

Memory

25.2MiB live, 25.2MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	268	12	280
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	268	13	281

Accuracy

99.9%

Counts

281 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.5%	(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)))
▶	60.4%	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
	60.4%	(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
	60.4%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	60.4%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
▶	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
	60.5%	(-.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))
	59.9%	(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
✓	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.6%	#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))
	99.5%	#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))
	99.1%	#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))
▶	98.2%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 555 to 326 computations (41.3% saved)

simplify153.0ms (1.2%)

Memory

-11.3MiB live, 102.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))
cost-diff	384	(-.f64 (+.f64 eps x) x)
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) 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	(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	(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)
cost-diff	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))
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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	695
0	101	683
1	157	609
2	313	591
3	911	591
4	4307	591
0	8161	584

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

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

localize330.0ms (2.5%)

Memory

30.0MiB live, 186.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
accuracy	0.06683208757593351	(cos.f64 (+.f64 eps x))
accuracy	0.07434796408644774	(sin.f64 (+.f64 eps x))
accuracy	25.23826717452837	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.06683208757593351	(cos.f64 (+.f64 eps x))
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
accuracy	25.358126097847435	(-.f64 (+.f64 eps x) x)
accuracy	0.00390625	(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
accuracy	0.08056588607446653	(tan.f64 (+.f64 eps x))
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
accuracy	25.26552661617361	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
accuracy	0	(sin.f64 eps)
accuracy	0	(cos.f64 eps)
accuracy	0.00390625	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	1.1248984451071593	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.0234375	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.14453125	(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))))
accuracy	0.24744459464961122	#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))
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

173.0ms	104×	1	valid
84.0ms	147×	0	valid
4.0ms	3×	2	valid
3.0ms	2×	3	valid

Compiler

Compiled 1 336 to 116 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 232.0ms

ival-pow: 60.0ms (25.8% of total)

ival-div: 58.0ms (25% of total)

ival-sin: 29.0ms (12.5% of total)

ival-mult: 17.0ms (7.3% of total)

adjust: 16.0ms (6.9% of total)

ival-add: 15.0ms (6.5% of total)

ival-tan: 8.0ms (3.4% of total)

const: 7.0ms (3% of total)

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

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

ival-cos: 6.0ms (2.6% 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)

series89.0ms (0.7%)

Memory

-25.7MiB live, 49.1MiB allocated

Counts

23 → 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 1/6 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 (-.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 (-.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)
(/.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))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
(-.f64 (+.f64 eps x) x)
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 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 (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))))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(sin.f64 (+.f64 eps x))

Outputs
-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
(+ 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)))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(/ (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)))
(+ (* 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))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin 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)))))))))
(/ 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) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ eps x)
(* 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 (* -1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(sin 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))))))))
(- (+ (* -1/2 (/ (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)))
(+ eps (* eps (+ (* 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)))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(* (cos x) (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(cos (+ eps x))
x
(* x (+ 1 (/ eps 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 (sin x) 3)
(sin (+ eps x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(* (cos x) (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin (- 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 (+ 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 (* 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 (* -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 (* 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)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (pow (cos x) 2) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(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))
(/ 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)
(+ (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 (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)))
(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))))))))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (+ 1 (/ x eps)))
(* (pow eps 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))))))
(* (pow eps 2) (- (+ 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))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (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))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* -1 (* (pow eps 3) (+ (* -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)))))
(/ 1 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* (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)) (+ (/ (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 (* -1 eps)))

Calls

6 calls:

Time	Variable		Point	Expression
34.0ms	eps	@	-inf	((+ (* (/ (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)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps 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)))) 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) 3) (sin (+ eps x)))
13.0ms	x	@	inf	((+ (* (/ (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)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps 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)))) 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) 3) (sin (+ eps x)))
9.0ms	x	@	-inf	((+ (* (/ (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)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps 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)))) 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) 3) (sin (+ eps x)))
9.0ms	eps	@	0	((+ (* (/ (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)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps 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)))) 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) 3) (sin (+ eps x)))
7.0ms	eps	@	inf	((+ (* (/ (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)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps 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)))) 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) 3) (sin (+ eps x)))

simplify201.0ms (1.5%)

Memory

-0.1MiB live, 114.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	667	4132
1	2077	3917
2	6960	3881
0	8188	3693

Stop Event

1×	iter limit
1×	node limit

Counts

148 → 146

Calls

Call 1

Inputs
-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
(+ 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)))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(/ (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)))
(+ (* 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))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin 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)))))))))
(/ 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) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ eps x)
(* 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 (* -1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(sin 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))))))))
(- (+ (* -1/2 (/ (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)))
(+ eps (* eps (+ (* 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)))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(* (cos x) (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(cos (+ eps x))
x
(* x (+ 1 (/ eps 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 (sin x) 3)
(sin (+ eps x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(* (cos x) (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin (- 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 (+ 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 (* 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 (* -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 (* 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)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (pow (cos x) 2) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(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))
(/ 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)
(+ (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 (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)))
(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))))))))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (+ 1 (/ x eps)))
(* (pow eps 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))))))
(* (pow eps 2) (- (+ 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))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (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))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* -1 (* (pow eps 3) (+ (* -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)))))
(/ 1 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* (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)) (+ (/ (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 (* -1 eps)))

Outputs
-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
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #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))
(/ (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 (sin.f64 eps) x) (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.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 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 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 (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (sin.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)))
(fma.f64 (*.f64 eps eps) x (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)))))
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(fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (-.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 -1/2 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.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 (/.f64 (sin.f64 x) (cos.f64 x)))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(fma.f64 (*.f64 (sin.f64 x) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (pow (cos x) 2) eps)
(/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/.f64 (fma.f64 (-.f64 (.f64 (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) eps) (*.f64 (cos.f64 x) (sin.f64 x))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/.f64 (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/120 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/18 binary64)))) (.f64 eps eps) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(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 (*.f64 (cos.f64 x) eps)) (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 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/2 binary64))) 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 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ 1 (cos x))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))
(fma.f64 (sin.f64 x) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(+ (* 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 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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)))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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)
(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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps (cos.f64 x))
(/ (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)))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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))))
(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 (sin.f64 x) #s(literal -1/2 binary64)) 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 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
(* (pow eps 3) (- (+ 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))))))
(*.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 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 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 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 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))))))
(*.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)) (fma.f64 (sin.f64 x) (/.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)) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.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 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/3 binary64)) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (/.f64 (sin.f64 x) eps) (fma.f64 (sin.f64 x) (/.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)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))) (pow.f64 eps #s(literal 3 binary64)))
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* (pow eps 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))))))
(.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 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 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))))) (.f64 eps eps))
(* (pow eps 2) (- (+ 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))))))
(.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)) (fma.f64 (sin.f64 x) (/.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)) 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 (+ (/ (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))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.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)) (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 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 eps eps)))) (+.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))
(- (/ (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 (* (pow eps 3) (+ (* -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)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 eps)) (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 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 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)))))))
(* -1 (* (pow eps 3) (+ (* -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)))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) (neg.f64 eps)) (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 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 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)))))))
(/ 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)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 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)
(* (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)) (+ (/ (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))))))
(.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 (/.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) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 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)))))) (.f64 eps eps))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))

rewrite322.0ms (2.5%)

Memory

41.0MiB live, 195.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	431
0	101	400
1	461	302
2	4003	294
0	9131	282

Stop Event

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

Counts

23 → 726

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

Outputs
(.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))) (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal -1/8 binary64)) (+.f64 (pow.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))))))
(/.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal -1/4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64)))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))) (fma.f64 #s(literal 1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 3 binary64)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (/.f64 #s(literal -1/2 binary64) (cos.f64 x)) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal -1/8 binary64)) (pow.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))
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(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(+.f64 (.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))) #s(literal 3/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (sin.f64 x)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x))
(*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 (sin.f64 x)))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 3/2 binary64))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))) (sin.f64 x)) #s(literal 2 binary64))
(/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 2 binary64))
(exp.f64 (fma.f64 (log.f64 (sin.f64 x)) #s(literal 3/2 binary64) (*.f64 (log.f64 (sin.f64 x)) #s(literal 3/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (sin.f64 x)) #s(literal 2 binary64) (log.f64 (sin.f64 x))))
(exp.f64 (+.f64 (log.f64 (sin.f64 x)) (log.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))
(exp.f64 (.f64 (.f64 (log.f64 (sin.f64 x)) #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal 3/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 3 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (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))) (+.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (.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 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 (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 (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)))

eval118.0ms (0.9%)

Memory: -26.6MiB live, 211.2MiB allocated
Compiler: Compiled 30 900 to 3 137 computations (89.8% saved)

prune23.0ms (0.2%)

Memory

19.8MiB live, 58.8MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	674	13	687
Fresh	5	2	7
Picked	5	0	5
Done	0	1	1
Total	684	16	700

Accuracy

100.0%

Counts

700 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.5%	(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)))
	60.4%	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
▶	99.9%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
▶	99.9%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
▶	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	99.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/120 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/18 binary64)))) (.f64 eps eps) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
	98.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
	60.5%	(-.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))
✓	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.9%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
	99.1%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	98.5%	#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)))) 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 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))
	98.3%	#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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
▶	98.5%	#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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
▶	98.2%	#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)))) 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))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) eps))

Compiler

Compiled 1 365 to 710 computations (48% saved)

simplify153.0ms (1.2%)

Memory

8.8MiB live, 166.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (+.f64 #s(literal 0 binary64) eps))
cost-diff	0	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
cost-diff	0	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	0	(tan.f64 (+.f64 eps x))
cost-diff	0	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x)))
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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) 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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
cost-diff	64	(fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x 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)))) 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)))) 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)))) 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	(sin.f64 (+.f64 #s(literal 0 binary64) eps))
cost-diff	0	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
cost-diff	0	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	764
0	98	738
1	169	666
2	424	654
3	1205	654
4	3925	654
5	7550	654
0	8097	630

Stop Event

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

Calls

Call 1

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

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

localize282.0ms (2.2%)

Memory

-2.0MiB live, 355.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
accuracy	0.01171875	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
accuracy	0.06683208757593351	(cos.f64 (+.f64 eps x))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
accuracy	0.08056588607446653	(tan.f64 (+.f64 eps x))
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
accuracy	25.26552661617361	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
accuracy	0.16015625	(*.f64 eps (+.f64 eps x))
accuracy	0.24744459464961122	#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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
accuracy	0.328125	(*.f64 #s(literal 1/3 binary64) eps)
accuracy	1.144403849795434	#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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x)))
accuracy	0	(*.f64 eps eps)
accuracy	0.2109375	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	0.24744459464961122	#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)))) 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	34.08567955367859	#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)))) 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	(cos.f64 x)
accuracy	0.00390625	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
accuracy	0.0078125	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
accuracy	0.06683208757593351	(cos.f64 (+.f64 eps x))

Samples

115.0ms	100×	1	valid
113.0ms	152×	0	valid
3.0ms	3×	2	valid
1.0ms	1×	3	valid

Compiler

Compiled 1 301 to 134 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

const: 44.0ms (22% of total)

ival-div: 33.0ms (16.5% of total)

ival-add: 33.0ms (16.5% of total)

ival-mult: 28.0ms (14% of total)

adjust: 18.0ms (9% of total)

ival-tan: 11.0ms (5.5% of total)

ival-pow: 10.0ms (5% of total)

ival-pow2: 7.0ms (3.5% of total)

ival-sub: 6.0ms (3% of total)

ival-cos: 4.0ms (2% of total)

ival-sin: 4.0ms (2% of total)

exact: 1.0ms (0.5% of total)

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

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

series46.0ms (0.4%)

Memory

19.6MiB live, 55.5MiB allocated

Counts

23 → 125

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	x	@	-inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 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)))) 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)))) 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) (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ 1 (/ 1 (- (tan (+ eps x)) (tan x)))) (/ 1 (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x)) (cos x) (* eps eps) (* 1/3 eps) (* eps (+ eps x)))
6.0ms	x	@	inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 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)))) 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)))) 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) (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ 1 (/ 1 (- (tan (+ eps x)) (tan x)))) (/ 1 (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x)) (cos x) (* eps eps) (* 1/3 eps) (* eps (+ eps x)))
5.0ms	eps	@	inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 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)))) 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)))) 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) (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ 1 (/ 1 (- (tan (+ eps x)) (tan x)))) (/ 1 (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x)) (cos x) (* eps eps) (* 1/3 eps) (* eps (+ eps x)))
5.0ms	eps	@	-inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 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)))) 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)))) 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) (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ 1 (/ 1 (- (tan (+ eps x)) (tan x)))) (/ 1 (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x)) (cos x) (* eps eps) (* 1/3 eps) (* eps (+ eps x)))
4.0ms	eps	@	0	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 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)))) 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)))) 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) (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (/ 1 (/ 1 (- (tan (+ eps x)) (tan x)))) (/ 1 (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x)) (cos x) (* eps eps) (* 1/3 eps) (* eps (+ eps x)))

simplify195.0ms (1.5%)

Memory

-38.8MiB live, 204.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	608	3924
1	1939	3695
2	6687	3657
0	8074	3496

Stop Event

1×	iter limit
1×	node limit

Counts

125 → 123

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos 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)))
(+ (* 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)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 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))))))))
eps
(+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))
(/ (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)))
(sin eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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))))
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)))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* 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 (+ (* 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)))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin eps) (cos x))
(cos (+ eps x))
(cos x)
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (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))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* 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))))
(* 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)))))
(/ (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)))
x
(+ x (* eps (+ 1 (* 4/3 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(/ 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)))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 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))))
(* 1/3 eps)
(* eps (+ eps x))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 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))))))
(* (pow eps 2) (- (+ 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))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (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))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(* (pow eps 2) (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin (neg (* -1 eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* (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)) (+ (/ (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))))))
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x)))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
(/ 1 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))

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

rewrite199.0ms (1.5%)

Memory

-33.0MiB live, 204.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	682
0	98	660
1	500	516
2	4706	504
0	8244	474

Stop Event

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

Counts

23 → 569

Calls

Call 1

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

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

eval109.0ms (0.8%)

Memory: 27.9MiB live, 108.6MiB allocated
Compiler: Compiled 48 763 to 2 809 computations (94.2% saved)

prune65.0ms (0.5%)

Memory

-14.6MiB live, 98.1MiB allocated

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	637	18	655
Fresh	5	5	10
Picked	3	2	5
Done	0	1	1
Total	645	26	671

Accuracy

100.0%

Counts

671 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.5%	(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)))
	60.4%	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
▶	100.0%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (cos.f64 x))
	98.7%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	98.5%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	99.5%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))
	99.9%	(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
▶	99.9%	(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
	99.9%	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	90.0%	(/.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) #s(literal -1 binary64))) (cos.f64 x))
✓	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
▶	98.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
	60.5%	(-.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))
✓	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	91.1%	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64)))
	99.1%	#s(approx (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	98.5%	#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)))) 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 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))
▶	98.3%	#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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
	98.5%	#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)))) 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 #s(approx (* eps (+ eps x)) (*.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
	98.5%	#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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 #s(literal 1 binary64) x)) x) x)) x))) eps eps))
	98.2%	#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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)) x))) eps eps))
	98.2%	#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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) x))) eps eps))
✓	98.2%	#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)))) 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))
	58.8%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)))
	58.6%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.f64 #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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 #s(literal 1/3 binary64) eps) eps))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)))
▶	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))

Compiler

Compiled 2 611 to 1 347 computations (48.4% saved)

simplify174.0ms (1.3%)

Memory

21.7MiB live, 139.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (cos.f64 x))
cost-diff	0	(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
cost-diff	0	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)
cost-diff	0	#s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
cost-diff	0	(+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))
cost-diff	64	(fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps)
cost-diff	128	(.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps)
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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x 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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) 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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
cost-diff	320	(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))
cost-diff	0	(sin.f64 (+.f64 #s(literal 0 binary64) eps))
cost-diff	0	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
cost-diff	0	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (cos.f64 x))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	925
0	121	910
1	205	814
2	485	800
3	1657	800
4	4089	800
0	8214	766

Stop Event

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

Calls

Call 1

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

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

localize350.0ms (2.7%)

Memory

0.0MiB live, 280.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(/.f64 (sin.f64 eps) (cos.f64 x))
accuracy	0.01171875	(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
accuracy	0.06683208757593351	(cos.f64 (+.f64 x eps))
accuracy	0	(cos.f64 x)
accuracy	0.015625	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
accuracy	0.5778029714440497	#s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))
accuracy	0.16015625	(*.f64 (+.f64 x eps) eps)
accuracy	0.24744459464961122	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))
accuracy	0.328125	(*.f64 #s(literal 1/3 binary64) eps)
accuracy	1.144403849795434	#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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x)))
accuracy	0	(*.f64 eps eps)
accuracy	0.140625	(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))
accuracy	0.24744459464961122	#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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
accuracy	35.02202273281554	#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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps)))
accuracy	0.00390625	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
accuracy	0.00390625	(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))
accuracy	0.0078125	(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
accuracy	0.0078125	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (cos.f64 x))

Samples

180.0ms	99×	1	valid
118.0ms	153×	0	valid
4.0ms	3×	2	valid
1.0ms	1×	3	valid

Compiler

Compiled 1 583 to 162 computations (89.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 263.0ms

ival-add: 90.0ms (34.3% of total)

const: 37.0ms (14.1% of total)

ival-mult: 35.0ms (13.3% of total)

ival-div: 24.0ms (9.1% of total)

ival-pow2: 20.0ms (7.6% of total)

adjust: 17.0ms (6.5% of total)

ival-pow: 14.0ms (5.3% of total)

ival-cos: 8.0ms (3% of total)

ival-sin: 7.0ms (2.7% of total)

ival-sub: 6.0ms (2.3% of total)

ival-tan: 4.0ms (1.5% of total)

exact: 1.0ms (0.4% of total)

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

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

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

series54.0ms (0.4%)

Memory

-21.7MiB live, 53.5MiB allocated

Counts

27 → 156

Calls

Call 1

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

Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 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)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ (* 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))))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))
eps
(+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))
(/ (cos eps) (sin eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin eps)))
(/ 1 eps)
(+ (* -1 (/ (pow x 2) eps)) (/ 1 eps))
(+ (* (pow x 2) (- (* 1/3 (/ (pow x 2) eps)) (/ 1 eps))) (/ 1 eps))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -2/45 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))) (/ 1 eps))) (/ 1 eps))
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)))
(sin eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))
(* -1 (* x (sin eps)))
(* x (+ (* -1 (sin eps)) (* 1/6 (* (pow x 2) (sin eps)))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin eps))) (* 1/6 (sin eps))))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* 1/6 (sin eps)) (* (pow x 2) (+ (* -1/120 (sin eps)) (* 1/5040 (* (pow x 2) (sin eps)))))))))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (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))))
(/ (sin eps) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
(/ (sin eps) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))
(* eps x)
(* x (+ eps (* 1/3 (/ (pow eps 2) x))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* 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 (+ (* 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 (+ (/ (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)))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(+ 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))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/ (pow (cos x) 2) eps)
(pow (cos x) 2)
(/ (sin eps) (cos x))
(cos x)
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))
(* -1 (* (sin eps) (sin x)))
(* x (+ eps (/ (pow eps 2) x)))
(cos (+ eps x))
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (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))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* 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))))
(* eps (+ x (* 1/3 eps)))
(* 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)))))
(/ (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)))
x
(+ x (* eps (+ 1 (* 4/3 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x))))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/6 (sin x)) (* (pow eps 2) (+ (* -1/120 (sin x)) (* 1/5040 (* (pow eps 2) (sin x)))))))))
(* 1/3 eps)
(* eps (+ eps 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) (+ 1/3 (/ x eps)))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 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))))))
(* (pow eps 2) (- (+ 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))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (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))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
(/ (sin (neg (* -1 eps))) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))
(sin (neg (* -1 eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* (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)) (+ (/ (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 (* (pow eps 3) (+ (* -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 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))) eps)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x)))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) 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))))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(cos (- x (* -1 eps)))

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	x	@	inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (sin (+ 0 eps)) (+ (* (* eps eps) 1/3) (* x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps) (+ (* (+ (* 4/3 (* (+ x eps) eps)) 1) x) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/ (pow (cos x) 2) eps) (pow (cos x) 2) (/ (/ (sin eps) (cos x)) (cos (+ x eps))) (/ (sin eps) (cos x)) (sin eps) (cos x) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (neg (sin eps)) (sin x)) (* 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 eps) (* (+ x eps) eps) (cos (+ x eps)))
12.0ms	eps	@	-inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (sin (+ 0 eps)) (+ (* (* eps eps) 1/3) (* x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps) (+ (* (+ (* 4/3 (* (+ x eps) eps)) 1) x) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/ (pow (cos x) 2) eps) (pow (cos x) 2) (/ (/ (sin eps) (cos x)) (cos (+ x eps))) (/ (sin eps) (cos x)) (sin eps) (cos x) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (neg (sin eps)) (sin x)) (* 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 eps) (* (+ x eps) eps) (cos (+ x eps)))
9.0ms	x	@	-inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (sin (+ 0 eps)) (+ (* (* eps eps) 1/3) (* x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps) (+ (* (+ (* 4/3 (* (+ x eps) eps)) 1) x) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/ (pow (cos x) 2) eps) (pow (cos x) 2) (/ (/ (sin eps) (cos x)) (cos (+ x eps))) (/ (sin eps) (cos x)) (sin eps) (cos x) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (neg (sin eps)) (sin x)) (* 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 eps) (* (+ x eps) eps) (cos (+ x eps)))
8.0ms	eps	@	inf	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (sin (+ 0 eps)) (+ (* (* eps eps) 1/3) (* x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps) (+ (* (+ (* 4/3 (* (+ x eps) eps)) 1) x) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/ (pow (cos x) 2) eps) (pow (cos x) 2) (/ (/ (sin eps) (cos x)) (cos (+ x eps))) (/ (sin eps) (cos x)) (sin eps) (cos x) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (neg (sin eps)) (sin x)) (* 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 eps) (* (+ x eps) eps) (cos (+ x eps)))
5.0ms	eps	@	0	((+ 0 eps) (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (sin (+ 0 eps)) (+ (* (* eps eps) 1/3) (* x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps) (+ (* (+ (* 4/3 (* (+ x eps) eps)) 1) x) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/ (pow (cos x) 2) eps) (pow (cos x) 2) (/ (/ (sin eps) (cos x)) (cos (+ x eps))) (/ (sin eps) (cos x)) (sin eps) (cos x) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (neg (sin eps)) (sin x)) (* 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/3 eps) (* (+ x eps) eps) (cos (+ x eps)))

simplify214.0ms (1.6%)

Memory

37.3MiB live, 185.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	689	3791
1	2206	3598
2	7234	3552
0	8376	3357

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 154

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* 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))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 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)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ (* 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))))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))
eps
(+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))
(/ (cos eps) (sin eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin eps)))
(/ 1 eps)
(+ (* -1 (/ (pow x 2) eps)) (/ 1 eps))
(+ (* (pow x 2) (- (* 1/3 (/ (pow x 2) eps)) (/ 1 eps))) (/ 1 eps))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -2/45 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))) (/ 1 eps))) (/ 1 eps))
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)))
(sin eps)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))
(* -1 (* x (sin eps)))
(* x (+ (* -1 (sin eps)) (* 1/6 (* (pow x 2) (sin eps)))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin eps))) (* 1/6 (sin eps))))))
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* 1/6 (sin eps)) (* (pow x 2) (+ (* -1/120 (sin eps)) (* 1/5040 (* (pow x 2) (sin eps)))))))))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (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))))
(/ (sin eps) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
(/ (sin eps) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))
(* eps x)
(* x (+ eps (* 1/3 (/ (pow eps 2) x))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* 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 (+ (* 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 (+ (/ (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)))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x))))
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2))))))
(+ 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))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/ (pow (cos x) 2) eps)
(pow (cos x) 2)
(/ (sin eps) (cos x))
(cos x)
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))
(* -1 (* (sin eps) (sin x)))
(* x (+ eps (/ (pow eps 2) x)))
(cos (+ eps x))
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos (- eps (* -1 x)))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (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))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* 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))))
(* eps (+ x (* 1/3 eps)))
(* 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)))))
(/ (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)))
x
(+ x (* eps (+ 1 (* 4/3 (pow x 2)))))
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x))))))
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/6 (sin x)) (* (pow eps 2) (+ (* -1/120 (sin x)) (* 1/5040 (* (pow eps 2) (sin x)))))))))
(* 1/3 eps)
(* eps (+ eps 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) (+ 1/3 (/ x eps)))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 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))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 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))))))
(* (pow eps 2) (- (+ 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))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (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))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ 1 (pow eps 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)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
(/ (sin (neg (* -1 eps))) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))
(sin (neg (* -1 eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* -1 (* (pow eps 3) (+ (* -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)))))
(* (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)) (+ (/ (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 (* (pow eps 3) (+ (* -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 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))) eps)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x)))
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x)))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) 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))))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(cos (- x (* -1 eps)))

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

rewrite272.0ms (2.1%)

Memory

-28.1MiB live, 254.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	847
0	121	846
1	579	623
2	5453	623
0	8701	577

Stop Event

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

Counts

27 → 663

Calls

Call 1

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

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

eval196.0ms (1.5%)

Memory: 3.1MiB live, 172.4MiB allocated
Compiler: Compiled 55 201 to 3 422 computations (93.8% saved)

prune52.0ms (0.4%)

Memory

3.3MiB live, 85.0MiB allocated

Pruning

28 alts after pruning (22 fresh and 6 done)

	Pruned	Kept	Total
New	695	13	708
Fresh	9	9	18
Picked	2	3	5
Done	0	3	3
Total	706	28	734

Accuracy

100.0%

Counts

734 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.4%	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
	100.0%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))) (cos.f64 x))
	99.9%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (.f64 (.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)))) (cos.f64 x))
	99.5%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))
	99.9%	(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
✓	99.9%	(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
	98.7%	(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
	98.5%	(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
	99.9%	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
	90.0%	(/.f64 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) #s(literal -1 binary64))) (cos.f64 x))
✓	60.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
✓	98.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
	98.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) eps)))
	98.2%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)))
	98.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) eps)))
	98.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) #s(approx (/ (pow (cos x) 2) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x x) eps)))))
	60.5%	(-.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))
✓	60.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	91.1%	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64)))
	100.0%	#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 (sin.f64 eps) (.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))
	99.1%	#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	98.5%	#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)))) 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 #s(approx (* eps (+ eps x)) (*.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
	98.2%	#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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)) x))) eps eps))
	98.2%	#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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) x))) eps eps))
✓	98.2%	#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)))) 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))
	98.3%	#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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 binary64) eps x))) eps eps))
	98.3%	#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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
✓	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))

Compiler

Compiled 3 704 to 1 044 computations (71.8% saved)

regimes47.0ms (0.4%)

Memory

12.3MiB live, 49.2MiB allocated

Counts

57 → 1

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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 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)))) 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 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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.f64 #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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 #s(literal 1/3 binary64) eps) eps))) (neg.f64 (*.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (* eps (+ eps x)) (*.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x 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)))) 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 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))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) #s(approx (/ (pow (cos x) 2) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x x) 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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 #s(literal 1 binary64) x)) x) x)) x))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (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)))
#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 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64)))
(-.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 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) #s(literal -1 binary64))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (.f64 (.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)))) (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)))
#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 (sin.f64 eps) (.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))) (cos.f64 x))
#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))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal 1/120 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/18 binary64)))) (.f64 eps eps) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (+.f64 (.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.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 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) 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 (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))

Calls

3 calls:

16.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms	eps
14.0ms	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)

regimes51.0ms (0.4%)

Memory

-2.1MiB live, 36.0MiB allocated

Counts

50 → 1

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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 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)))) 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 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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.f64 #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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 #s(literal 1/3 binary64) eps) eps))) (neg.f64 (*.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (* eps (+ eps x)) (*.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x 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)))) 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 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))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) #s(approx (/ (pow (cos x) 2) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x x) 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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 #s(literal 1 binary64) x)) x) x)) x))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (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)))
#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 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64)))
(-.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 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) #s(literal -1 binary64))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (.f64 (.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps)))) (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)))

Outputs

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

Calls

3 calls:

24.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms	x
12.0ms	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)

regimes44.0ms (0.3%)

Memory

-26.1MiB live, 54.9MiB allocated

Counts

48 → 1

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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 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)))) 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 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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.f64 #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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 #s(literal 1/3 binary64) eps) eps))) (neg.f64 (*.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (* eps (+ eps x)) (*.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x 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)))) 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 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))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) #s(approx (/ (pow (cos x) 2) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x x) 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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 #s(literal 1 binary64) x)) x) x)) x))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (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)))
#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 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64)))
(-.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 (exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) #s(literal -1 binary64))) (cos.f64 x))

Outputs
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))

Calls

3 calls:

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

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)

regimes53.0ms (0.4%)

Memory

9.4MiB live, 47.8MiB allocated

Counts

37 → 1

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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 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)))) 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 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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.f64 #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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 #s(literal 1/3 binary64) eps) eps))) (neg.f64 (*.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (* eps (+ eps x)) (*.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x 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)))) 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 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))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) #s(approx (/ (pow (cos x) 2) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x x) 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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 #s(literal 1 binary64) x)) x) x)) x))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))

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

Calls

3 calls:

32.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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)

regimes27.0ms (0.2%)

Memory

30.9MiB live, 30.9MiB allocated

Counts

32 → 1

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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x 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)))) 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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 #s(literal 1/3 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)))) 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 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)))) 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 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (*.f64 x x) #s(literal 4/3 binary64)) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.f64 #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)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 #s(literal 1/3 binary64) eps) eps))) (neg.f64 (*.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (* eps (+ eps x)) (*.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x 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)))) 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 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))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) #s(approx (/ (pow (cos x) 2) eps) (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 x x) 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)))) 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 (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps))) eps) eps)) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (.f64 (+.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)))) 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 #s(literal 4/3 binary64) (.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) #s(literal 1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 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)))) 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 #s(approx (+ (* (+ (* (* eps (+ eps x)) 4/3) 1) x) eps) (.f64 (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 #s(literal 1 binary64) x)) x) x)) x))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (/ (sin (+ 0 eps)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (cos x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

-14.1MiB live, 24.1MiB allocated

Counts

20 → 1

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

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

Calls

3 calls:

6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	x
5.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

-18.2MiB live, 18.8MiB allocated

Counts

17 → 1

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

Calls

3 calls:

14.0ms	eps
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	x

Results

Accuracy	Segments	Branch
98.5%	1	`eps`
98.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.5%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

9 → 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`
98.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

15.6MiB live, 15.6MiB allocated

Accuracy

Total -25.6b remaining (-2308.5%)

Threshold costs -25.6b (-2308.5%)

Counts

8 → 1

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify45.0ms (0.3%)

Memory

1.7MiB live, 46.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	475
1	145	475
2	147	475
3	148	475

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (11.6%)

Memory

-13.3MiB live, 984.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	950
1	464	884
2	1535	873
3	5933	841
0	8521	794
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	689	3791
1	2206	3598
2	7234	3552
0	8376	3357
0	608	3924
1	1939	3695
2	6687	3657
0	8074	3496
0	68	682
0	98	660
1	500	516
2	4706	504
0	8244	474
0	55	431
0	101	400
1	461	302
2	4003	294
0	9131	282
0	81	847
0	121	846
1	579	623
2	5453	623
0	8701	577
0	667	4132
1	2077	3917
2	6960	3881
0	8188	3693

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×	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

Compiler

Compiled 915 to 388 computations (57.6% saved)

preprocess62.0ms (0.5%)

Memory: -12.0MiB live, 105.0MiB allocated
Compiler: Compiled 982 to 274 computations (72.1% 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%)

analyze44.0ms (0.3%)

sample6.8s (52.1%)

explain175.0ms (1.4%)

preprocess25.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize55.0ms (0.4%)

series11.0ms (0.1%)

simplify162.0ms (1.2%)

rewrite146.0ms (1.1%)

eval78.0ms (0.6%)

prune12.0ms (0.1%)

simplify153.0ms (1.2%)

localize330.0ms (2.5%)

series89.0ms (0.7%)

simplify201.0ms (1.5%)

rewrite322.0ms (2.5%)

eval118.0ms (0.9%)

prune23.0ms (0.2%)

simplify153.0ms (1.2%)

localize282.0ms (2.2%)

series46.0ms (0.4%)

simplify195.0ms (1.5%)

rewrite199.0ms (1.5%)

eval109.0ms (0.8%)

prune65.0ms (0.5%)

simplify174.0ms (1.3%)

localize350.0ms (2.7%)

series54.0ms (0.4%)

simplify214.0ms (1.6%)

rewrite272.0ms (2.1%)

eval196.0ms (1.5%)

prune52.0ms (0.4%)

regimes47.0ms (0.4%)

regimes51.0ms (0.4%)

regimes44.0ms (0.3%)

regimes53.0ms (0.4%)

regimes27.0ms (0.2%)

regimes21.0ms (0.2%)

regimes25.0ms (0.2%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

simplify45.0ms (0.3%)

soundness1.5s (11.6%)

preprocess62.0ms (0.5%)

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