Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze64.0ms (0.4%)

Memory

-20.9MiB live, 70.2MiB 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)

sample5.9s (39.9%)

Memory

-179.8MiB live, 8 647.3MiB allocated

Samples

2.9s	26 447×	0	invalid
818.0ms	2 831×	1	valid
568.0ms	5 425×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.2s

ival-tan: 645.0ms (20.2% of total)

const: 611.0ms (19.1% of total)

ival-mult: 505.0ms (15.8% of total)

ival-add: 294.0ms (9.2% of total)

ival-fabs: 258.0ms (8.1% of total)

ival-<=: 227.0ms (7.1% of total)

ival-sub: 197.0ms (6.2% of total)

ival-<: 191.0ms (6% of total)

adjust: 106.0ms (3.3% of total)

ival-and: 102.0ms (3.2% of total)

exact: 46.0ms (1.4% of total)

ival-assert: 13.0ms (0.4% of total)

Bogosity

explain126.0ms (0.9%)

Memory

4.5MiB live, 199.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
220	3	(-1.416919849175757e-287 1.3021226862724824e-289)	4	(2.1834476938807615e-101 2.357669797071679e-103)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
2	0	-	1	(32.20894738896712 8.664518947479058e-9)	`(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	219	5
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	216	4
-	3	33

Precision

0.9863013698630136

Recall

0.9818181818181818

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	216	3	1
-	3	2	31

Precision?

0.9776785714285714

Recall?

0.9954545454545455

Freqs

test

number	freq
0	37
1	218
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms	162×	1	valid
23.0ms	6×	3	valid
18.0ms	342×	0	valid
3.0ms	2×	2	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-tan: 33.0ms (53% of total)

ival-sub: 19.0ms (30.5% of total)

ival-add: 5.0ms (8% of total)

adjust: 4.0ms (6.4% of total)

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

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

preprocess40.0ms (0.3%)

Memory

2.0MiB live, 39.8MiB allocated

Algorithm

1×	egg-herbie

Rules

160×	`lower-fma.f64`
160×	`lower-fma.f32`
130×	`sub-neg`
102×	`cancel-sub-sign`
96×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	42	35
2	112	35
3	270	35
4	462	35
5	516	35
6	539	35
7	546	35
0	6	7
0	10	7
1	15	7
2	28	7
3	56	7
4	114	7
5	191	7
6	228	7
7	235	7
0	235	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))

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB 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))

Rules

160×	`lower-fma.f64`
160×	`lower-fma.f32`
96×	`lower-*.f64`
96×	`lower-*.f32`
64×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	28	18
3	56	18
4	114	18
5	191	18
6	228	18
7	235	18
0	235	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))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)

localize93.0ms (0.6%)

Memory

-36.3MiB live, 50.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.07219329735525833	(tan.f64 (+.f64 x eps))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

65.0ms	81×	1	valid
11.0ms	3×	3	valid
8.0ms	171×	0	valid
1.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-add: 38.0ms (49% of total)

ival-sub: 22.0ms (28.4% of total)

ival-tan: 16.0ms (20.6% of total)

adjust: 2.0ms (2.6% of total)

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

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

series11.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))>
#<alt (tan.f64 (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt (tan.f64 x)>

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

Calls

21 calls:

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

simplify867.0ms (5.9%)

Memory

-89.3MiB live, 550.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 644×	`lower-fma.f64`
11 644×	`lower-fma.f32`
4 420×	`lower-*.f64`
4 420×	`lower-*.f32`
4 404×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1399
1	548	1330
2	2246	1322
0	8168	1258

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

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)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ 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)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos 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)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (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)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (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)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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 x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

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

rewrite273.0ms (1.9%)

Memory

31.1MiB live, 507.2MiB allocated

Rules

4 262×	`lower-*.f64`
4 262×	`lower-*.f32`
3 614×	`lower-fma.f64`
3 614×	`lower-fma.f32`
3 578×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	52	16
2	446	16
3	6895	16
0	8417	16

Stop Event

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

Counts

4 → 326

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

eval50.0ms (0.3%)

Memory: -22.0MiB live, 133.0MiB allocated
Compiler: Compiled 11 378 to 1 218 computations (89.3% saved)

prune67.0ms (0.5%)

Memory

-8.1MiB live, 160.0MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	384	19	403
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	384	20	404

Accuracy

100.0%

Counts

404 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.7%	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
	62.7%	(fma.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))
	62.5%	(fma.f64 (sin.f64 (neg.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 (+.f64 x eps)))
	61.5%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶	62.5%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	62.5%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x))))
	62.6%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	62.5%	(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
	62.6%	(-.f64 (+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
▶	37.5%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 eps x))) (tan.f64 x))
	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (*.f64 x #s(literal 2/15 binary64)) #s(literal 1/3 binary64)) x) x)))
▶	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
	98.9%	(+.f64 (+.f64 (neg.f64 (tan.f64 x)) (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))))
▶	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.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 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.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 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 905 to 426 computations (52.9% saved)

simplify429.0ms (2.9%)

Memory

2.2MiB live, 598.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (tan.f64 x) (tan.f64 eps))
cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
cost-diff	128	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
cost-diff	192	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (-.f64 (+.f64 x eps) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
cost-diff	384	(-.f64 (+.f64 x eps) x)
cost-diff	0	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 eps x))) (tan.f64 x))
cost-diff	128	(-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x)))
cost-diff	256	(*.f64 (neg.f64 x) (neg.f64 x))
cost-diff	1088	(/.f64 (-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 eps x))
cost-diff	0	#s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
cost-diff	6784	(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
cost-diff	13376	(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.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 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.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 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
cost-diff	20032	(+.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 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/6 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 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))

Rules

13 950×	`lower-fma.f32`
13 934×	`lower-fma.f64`
4 218×	`lower--.f32`
4 206×	`lower--.f64`
3 214×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	690
0	106	676
1	241	614
2	813	567
3	3511	505
0	8633	494

Stop Event

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

Calls

Call 1

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

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

localize259.0ms (1.8%)

Memory

46.3MiB live, 392.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 (tan.f64 x))
accuracy	0.0078125	(*.f64 (tan.f64 x) (tan.f64 eps))
accuracy	0.01953125	(+.f64 (tan.f64 x) (tan.f64 eps))
accuracy	23.901158122232932	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
accuracy	0.01171875	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	23.96972852167959	(-.f64 (+.f64 x eps) x)
accuracy	0.06766378162065376	(-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x)))
accuracy	0.07219329735525833	(tan.f64 (/.f64 (-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 eps x)))
accuracy	23.918482892439503	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 eps x))) (tan.f64 x))
accuracy	26.86809715252398	(/.f64 (-.f64 (.f64 eps eps) (.f64 (neg.f64 x) (neg.f64 x))) (-.f64 eps x))
accuracy	0.07219329735525833	(tan.f64 (+.f64 x eps))
accuracy	0.2265625	(.f64 #s(literal 1/3 binary64) (.f64 x x))
accuracy	0.9033645080441755	#s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
accuracy	0.015625	(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy	0.109375	(fma.f64 eps (fma.f64 eps (+.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 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.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 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.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 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.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 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
accuracy	0.9765625	(+.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 #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/6 binary64)))

Samples

77.0ms	87×	1	valid
67.0ms	163×	0	valid
33.0ms	4×	3	valid
7.0ms	2×	2	valid

Compiler

Compiled 618 to 59 computations (90.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-tan: 40.0ms (26.2% of total)

ival-mult: 31.0ms (20.3% of total)

ival-add: 20.0ms (13.1% of total)

adjust: 13.0ms (8.5% of total)

ival-div: 11.0ms (7.2% of total)

ival-sub: 9.0ms (5.9% of total)

const: 8.0ms (5.2% of total)

ival-sin: 6.0ms (3.9% of total)

ival-pow2: 6.0ms (3.9% of total)

ival-cos: 5.0ms (3.3% of total)

ival-neg: 3.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series92.0ms (0.6%)

Memory

12.4MiB live, 145.2MiB allocated

Counts

27 → 564

Calls

Call 1

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

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/3 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/3 (* 2/9 (pow x 2)))))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/9 (* 17/135 (pow x 2)))))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt 1/3>
#<alt (+ 1/3 (* 4/3 (pow x 2)))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))>
#<alt (+ eps (* 1/3 (pow eps 3)))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 4/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin x) (cos x))>
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
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#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 (pow x 2))>
#<alt (- (pow eps 2) (pow x 2))>
#<alt (- (pow eps 2) (pow x 2))>
#<alt (- (pow eps 2) (pow x 2))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (pow x 2) (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (pow x 2) (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (+ (* -1 (pow x 2)) (pow eps 2))>
#<alt (+ (* -1 (pow x 2)) (pow eps 2))>
#<alt (+ (* -1 (pow x 2)) (pow eps 2))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 1))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (- eps x))) (cos (/ (- (pow eps 2) (pow x 2)) (- eps x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (- eps x))) (cos (/ (- (pow eps 2) (pow x 2)) (- eps x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (- eps x))) (cos (/ (- (pow eps 2) (pow x 2)) (- eps x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (- eps x))) (cos (/ (- (pow eps 2) (pow x 2)) (- eps x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps))))) (cos (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps)))))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps))))) (cos (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps)))))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps))))) (cos (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps)))))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps))))) (cos (* -1 (/ (- (pow eps 2) (pow x 2)) (+ x (* -1 eps)))))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (- eps x))) (cos (/ (- (pow eps 2) (pow x 2)) (- eps x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (- eps x))) (cos (/ (- (pow eps 2) (pow x 2)) (- eps x)))) (/ (sin x) (cos x)))>
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#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (- eps x))) (cos (/ (- (pow eps 2) (pow x 2)) (- eps x)))) (/ (sin x) (cos x)))>
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#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (+ eps (* -1 x)))) (cos (/ (- (pow eps 2) (pow x 2)) (+ eps (* -1 x))))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (+ eps (* -1 x)))) (cos (/ (- (pow eps 2) (pow x 2)) (+ eps (* -1 x))))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (/ (- (pow eps 2) (pow x 2)) (+ eps (* -1 x)))) (cos (/ (- (pow eps 2) (pow x 2)) (+ eps (* -1 x))))) (/ (sin x) (cos x)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ eps (pow (cos x) 2))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt 1>
#<alt (+ 1 (/ (* x (sin eps)) (cos eps)))>
#<alt (+ 1 (* x (- (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)) (* -1 (/ (sin eps) (cos eps))))))>
#<alt (+ 1 (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (sin eps) (cos eps))))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt 1>
#<alt (+ 1 (/ (* eps (sin x)) (cos x)))>
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#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))>
#<alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (pow (cos x) 2)>
#<alt (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ x (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (+ eps (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (* -1 x)>
#<alt (* x (- (* -1/3 (pow x 2)) 1))>
#<alt (* x (- (* (pow x 2) (- (* -2/15 (pow x 2)) 1/3)) 1))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/315 (pow x 2)) 2/15)) 1/3)) 1))>
#<alt (* -1 (/ (sin x) (cos x)))>
#<alt (* -1 (/ (sin x) (cos x)))>
#<alt (* -1 (/ (sin x) (cos x)))>
#<alt (* -1 (/ (sin x) (cos x)))>
#<alt (* -1 (/ (sin x) (cos x)))>
#<alt (* -1 (/ (sin x) (cos x)))>
#<alt (* -1 (/ (sin x) (cos x)))>
#<alt (* -1 (/ (sin x) (cos x)))>

Calls

141 calls:

Time	Variable		Point	Expression
16.0ms	x	@	-inf	(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (neg (tan x)))
6.0ms	x	@	inf	(+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2))
5.0ms	eps	@	-inf	(+ (* eps (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
2.0ms	x	@	inf	(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (neg (tan x)))
2.0ms	x	@	inf	(+ (* eps (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)

simplify373.0ms (2.5%)

Memory

14.4MiB live, 618.9MiB allocated

Algorithm

1×	egg-herbie

Rules

6 974×	`lower-fma.f64`
6 974×	`lower-fma.f32`
5 484×	`lower-*.f64`
5 484×	`lower-*.f32`
4 086×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	680	11088
1	2760	10914
0	8567	10532

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 525

Calls

Call 1

Inputs
1/2
(+ 1/2 (* 1/3 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/3 (* 2/9 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/9 (* 17/135 (pow x 2)))))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1/2 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 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)))))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) 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)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
x
(* x (+ 1 (* 4/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ 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)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos 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)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
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(cos (- x (* -1 eps)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(/ (sin eps) (cos eps))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(* -1 x)
(* x (- (* -1/3 (pow x 2)) 1))
(* x (- (* (pow x 2) (- (* -2/15 (pow x 2)) 1/3)) 1))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/315 (pow x 2)) 2/15)) 1/3)) 1))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))

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

rewrite550.0ms (3.7%)

Memory

-44.1MiB live, 416.1MiB allocated

Rules

6 308×	`lower-fma.f32`
6 292×	`lower-fma.f64`
4 786×	`lower-*.f32`
4 772×	`lower-*.f64`
2 240×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	508
0	106	468
1	523	284
2	5378	280
0	8509	273

Stop Event

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

Counts

27 → 1 134

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

Outputs
(+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))
(+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 (.f64 #s(literal -1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) (/.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))) (*.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))
(+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (neg.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))))
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/6 binary64)))
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)) (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))))
(-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1/6 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1/6 binary64)) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal -1/6 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #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))
(fma.f64 #s(literal -1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))))
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)))
(fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)))
(fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64)))
(fma.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))))
(fma.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1/6 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (cos.f64 x)) (+.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))))
(fma.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (cos.f64 x)) (/.f64 #s(literal -1/6 binary64) (cos.f64 x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (cos.f64 x)) (/.f64 #s(literal -1/6 binary64) (cos.f64 x)) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/6 binary64))) (.f64 #s(literal 1/36 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal -1/216 binary64) (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))
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(+.f64 (tan.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(+.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) (tan.f64 eps)) (tan.f64 x))
(+.f64 (.f64 (tan.f64 x) #s(literal 1 binary64)) (.f64 (tan.f64 eps) #s(literal 1 binary64)))
(+.f64 (.f64 (tan.f64 eps) #s(literal 1 binary64)) (.f64 (tan.f64 x) #s(literal 1 binary64)))
(-.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)))
(-.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 eps))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (neg.f64 (tan.f64 eps))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (tan.f64 eps))
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (neg.f64 (neg.f64 (tan.f64 eps))))
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 #s(literal 1 binary64) (tan.f64 eps) (tan.f64 x))
(fma.f64 (tan.f64 x) #s(literal 1 binary64) (*.f64 (tan.f64 eps) #s(literal 1 binary64)))
(fma.f64 (tan.f64 eps) #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(literal 1 binary64)))
(fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (tan.f64 x))
(fma.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)) (tan.f64 eps))
(fma.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)) (neg.f64 (neg.f64 (tan.f64 eps))))
(fma.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 (sin.f64 (neg.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 eps))
(fma.f64 (sin.f64 (neg.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (neg.f64 (neg.f64 (tan.f64 eps))))
(fma.f64 (sin.f64 (neg.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (neg.f64 (neg.f64 (tan.f64 eps))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (tan.f64 eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (neg.f64 (neg.f64 (tan.f64 eps))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))
(/.f64 (sin.f64 (+.f64 x eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 eps) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (sin.f64 eps))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 eps)))
(/.f64 (fma.f64 (sin.f64 (neg.f64 x)) (cos.f64 eps) (.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 eps)))
(/.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (.f64 (cos.f64 eps) #s(literal 1 binary64))) (.f64 (cos.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (fma.f64 (sin.f64 eps) (neg.f64 (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 (neg.f64 x)))) (.f64 (cos.f64 eps) (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (tan.f64 x) (tan.f64 eps))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (neg.f64 (tan.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (neg.f64 (tan.f64 eps)) (neg.f64 (tan.f64 eps)) (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))))))
(/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (tan.f64 eps) (tan.f64 x)))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (tan.f64 eps)) (neg.f64 (tan.f64 eps)))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(pow.f64 (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 x) (tan.f64 eps))))
(+.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 x)))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
(neg.f64 (tan.f64 x))
(/.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (sin.f64 (neg.f64 x)) (cos.f64 x))
(/.f64 (sin.f64 (neg.f64 x)) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (sin.f64 (neg.f64 x))) (neg.f64 (cos.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(pow.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (tan.f64 x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (tan.f64 x))
(*.f64 (sin.f64 (neg.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))

eval433.0ms (2.9%)

Memory: 29.2MiB live, 374.8MiB allocated
Compiler: Compiled 65 685 to 4 471 computations (93.2% saved)

prune203.0ms (1.4%)

Memory

-14.4MiB live, 382.4MiB allocated

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	1 822	11	1 833
Fresh	14	0	14
Picked	5	0	5
Done	0	1	1
Total	1 841	12	1 853

Accuracy

100.0%

Counts

1 853 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	99.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
▶	99.7%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	99.3%	#s(approx (- (tan (/ (- (* eps eps) (* (neg x) (neg x))) (- eps x))) (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))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 eps (fma.f64 (+.f64 #s(literal -1/6 binary64) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) eps (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6)) #s(literal 1/3 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x eps))) eps))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))

Compiler

Compiled 527 to 272 computations (48.4% saved)

simplify348.0ms (2.4%)

Memory

-5.1MiB live, 615.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

14 286×	`lower-fma.f32`
14 272×	`lower-fma.f64`
4 126×	`lower--.f64`
4 126×	`lower--.f32`
3 490×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	850
0	99	854
1	238	782
2	798	707
3	3312	657
0	8340	640

Stop Event

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

Calls

Call 1

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

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

localize252.0ms (1.7%)

Memory

-14.2MiB live, 309.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.015625	(pow.f64 (cos.f64 x) #s(literal 3 binary64))
accuracy	0.0234375	(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
accuracy	0.21072892870839285	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0.14343639836813848	#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
accuracy	0.18359375	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
accuracy	0.13671875	(fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
accuracy	0.17578125	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	1.2060271157130906	#s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
accuracy	0.00390625	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps)
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
accuracy	0.17578125	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	31.424916395330225	#s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
accuracy	0	#s(approx (sin (- (+ x eps) x)) (sin.f64 eps))
accuracy	0.01171875	(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))

Samples

104.0ms	81×	1	valid
77.0ms	171×	0	valid
4.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 582 to 59 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 157.0ms

ival-mult: 55.0ms (35% of total)

ival-add: 29.0ms (18.4% of total)

ival-pow2: 18.0ms (11.4% of total)

const: 12.0ms (7.6% of total)

ival-div: 11.0ms (7% of total)

adjust: 11.0ms (7% of total)

ival-tan: 6.0ms (3.8% of total)

ival-sin: 6.0ms (3.8% of total)

ival-cos: 4.0ms (2.5% of total)

ival-sub: 3.0ms (1.9% of total)

ival-pow: 3.0ms (1.9% of total)

exact: 1.0ms (0.6% of total)

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

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

series28.0ms (0.2%)

Memory

-0.7MiB live, 36.8MiB allocated

Counts

23 → 468

Calls

Call 1

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

Outputs
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ eps (pow (cos x) 2))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))>
#<alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (pow (cos x) 2)>
#<alt (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
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#<alt (* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))>
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#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (/ (* (pow eps 2) (sin x)) (pow (cos x) 3))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (/ (* (pow eps 2) (sin x)) (pow (cos x) 3))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt eps>
#<alt (+ eps (* (pow eps 2) x))>
#<alt (+ eps (* x (+ (* eps x) (pow eps 2))))>
#<alt (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* -1/6 eps) (* -3/2 eps)))))) (pow eps 2))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ eps (pow (cos x) 2))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ 1 (pow (cos x) 2))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (/ (* eps (sin x)) (pow (cos x) 3))>
#<alt (* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (/ (* eps (sin x)) (pow (cos x) 3))>
#<alt (* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))>
#<alt 1>
#<alt (+ 1 (* eps x))>
#<alt (+ 1 (* x (+ eps x)))>
#<alt (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* -1/6 eps) (* -3/2 eps))))))))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt x>
#<alt (* x (+ 1 (* 4/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (/ (sin x) (pow (cos x) 3))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt 1>
#<alt (+ 1 (* -3/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 7/8 (pow x 2)) 3/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))>
#<alt (pow (cos x) 3)>
#<alt (pow (cos x) 3)>
#<alt (pow (cos x) 3)>
#<alt (pow (cos x) 3)>
#<alt (pow (cos x) 3)>
#<alt (pow (cos x) 3)>
#<alt (pow (cos x) 3)>
#<alt (pow (cos x) 3)>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>

Calls

117 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))))
2.0ms	x	@	-inf	(* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))))
1.0ms	eps	@	0	(* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))))
1.0ms	eps	@	inf	(* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))))
1.0ms	eps	@	-inf	(* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))))

simplify371.0ms (2.5%)

Memory

35.4MiB live, 422.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 672×	`lower-fma.f64`
9 672×	`lower-fma.f32`
5 634×	`lower-*.f64`
5 634×	`lower-*.f32`
4 024×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	491	11125
1	2052	10047
0	8361	9548

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 462

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)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos 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))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* 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))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
eps
(* 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))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin 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)))))))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(/ (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)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ 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)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos 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)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) 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)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 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)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ 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)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos 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)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
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(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
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(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* 1/3 (pow eps 2))
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(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(* 1/3 (pow eps 2))
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(/ (sin eps) (cos eps))
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eps
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eps
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(/ eps (pow (cos x) 2))
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eps
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(/ 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))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (pow (cos x) 2))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(/ (* eps (sin x)) (pow (cos x) 3))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(/ (* eps (sin x)) (pow (cos x) 3))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
1
(+ 1 (* eps x))
(+ 1 (* x (+ eps x)))
(+ 1 (* x (+ eps (* x (+ 1 (* x (- (* -1/6 eps) (* -3/2 eps))))))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
x
(* x (+ 1 (* 4/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(/ (sin x) (pow (cos x) 3))
(/ (sin x) (pow (cos x) 3))
(/ (sin x) (pow (cos x) 3))
(/ (sin x) (pow (cos x) 3))
(/ (sin x) (pow (cos x) 3))
(/ (sin x) (pow (cos x) 3))
(/ (sin x) (pow (cos x) 3))
(/ (sin x) (pow (cos x) 3))
(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))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 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))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
1
(+ 1 (* -3/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 7/8 (pow x 2)) 3/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))
(pow (cos x) 3)
(pow (cos x) 3)
(pow (cos x) 3)
(pow (cos x) 3)
(pow (cos x) 3)
(pow (cos x) 3)
(pow (cos x) 3)
(pow (cos x) 3)
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)))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)

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 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (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 x (fma.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 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)))) (/.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 x (fma.f64 x (+.f64 (fma.f64 x (neg.f64 (-.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (-.f64 (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (cos.f64 eps)) (/.f64 (.f64 (sin.f64 eps) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 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)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps 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))))
(*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (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))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (+.f64 (/.f64 #s(literal 1/2 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)))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (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))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 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)))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))) (neg.f64 eps) (+.f64 (+.f64 (/.f64 #s(literal 1/2 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)))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 x (neg.f64 (fma.f64 (cos.f64 eps) x (sin.f64 eps))) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(fma.f64 x (fma.f64 x (-.f64 (.f64 (sin.f64 eps) (.f64 #s(literal 2/3 binary64) x)) (cos.f64 eps)) (sin.f64 (neg.f64 eps))) (cos.f64 eps))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (neg.f64 eps) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) eps) (.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))) (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 eps (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) (.f64 eps (sin.f64 x))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(/ (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 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (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 x (fma.f64 (*.f64 (sin.f64 eps) x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.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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(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 eps (fma.f64 (*.f64 eps (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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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(- (/ (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))) (/ (sin x) (cos x)))
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(- (/ (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))) (/ (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)))) (/ (sin x) (cos x)))
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(-.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)))) (/ (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)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 (*.f64 eps (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.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) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 eps (cos.f64 x))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
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(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 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 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 eps (cos.f64 x))) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 eps eps)))))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (*.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(- (/ (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 (* -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)))) (/ (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)))) (/ (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)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 eps (fma.f64 (*.f64 eps (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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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(- (/ (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))) (/ (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))) (/ (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))) (/ (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)))) (/ (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)))) (/ (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)))) (/ (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)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 (*.f64 eps (sin.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.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) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.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) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 eps (cos.f64 x))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 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 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 eps (cos.f64 x))) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 eps eps)))))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 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 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 eps (cos.f64 x))) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 eps eps)))))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (*.f64 eps eps)))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
(neg.f64 (.f64 eps (.f64 (.f64 eps eps) (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 eps (cos.f64 x))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(neg.f64 (.f64 (.f64 eps (*.f64 eps eps)) (-.f64 (neg.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(neg.f64 (.f64 (.f64 eps (*.f64 eps eps)) (-.f64 (neg.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps))))
(+ eps (* 1/3 (pow eps 3)))
(fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64))) eps)
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps 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))))
(*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (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))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (+.f64 (/.f64 #s(literal 1/2 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)))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (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))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 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)))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))) (neg.f64 eps) (+.f64 (+.f64 (/.f64 #s(literal 1/2 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)))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/ 1 (pow (cos x) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (* eps (sin x)) (pow (cos x) 3))
(/.f64 (*.f64 eps (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(.f64 eps (+.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(.f64 eps (+.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(.f64 eps (+.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(/ (* eps (sin x)) (pow (cos x) 3))
(/.f64 (*.f64 eps (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(neg.f64 (.f64 eps (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(neg.f64 (.f64 eps (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(neg.f64 (.f64 eps (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* eps x))
(fma.f64 eps x #s(literal 1 binary64))
(+ 1 (* x (+ eps x)))
(fma.f64 x (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ eps (* x (+ 1 (* x (- (* -1/6 eps) (* -3/2 eps))))))))
(fma.f64 x (fma.f64 x (fma.f64 eps (*.f64 #s(literal 4/3 binary64) x) #s(literal 1 binary64)) eps) #s(literal 1 binary64))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
x
(* x (+ 1 (* 4/3 (pow x 2))))
(fma.f64 x (.f64 #s(literal 4/3 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 (*.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) x) x)
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 248/315 binary64) #s(literal 17/15 binary64))) #s(literal 4/3 binary64)) (.f64 (.f64 x x) x) x)
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/ (sin x) (pow (cos x) 3))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 x (-.f64 (.f64 (cos.f64 eps) (.f64 #s(literal -1/2 binary64) x)) (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 x (fma.f64 x (fma.f64 (sin.f64 eps) (.f64 #s(literal 1/6 binary64) x) (.f64 (cos.f64 eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 eps))) (cos.f64 eps))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 eps (-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (sin.f64 x)) (cos.f64 x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
1
#s(literal 1 binary64)
(+ 1 (* -3/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -3/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 7/8 (pow x 2)) 3/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 7/8 binary64) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -61/240 binary64) #s(literal 7/8 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(pow (cos x) 3)
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))

rewrite330.0ms (2.2%)

Memory

3.7MiB live, 358.9MiB allocated

Rules

4 964×	`lower-fma.f32`
4 950×	`lower-fma.f64`
4 944×	`lower-*.f32`
4 934×	`lower-*.f64`
2 182×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	773
0	99	749
1	514	505
2	4952	493
0	8152	472

Stop Event

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

Counts

23 → 350

Calls

Call 1

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

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

eval110.0ms (0.7%)

Memory: 4.0MiB live, 191.8MiB allocated
Compiler: Compiled 25 819 to 1 537 computations (94% saved)

prune82.0ms (0.6%)

Memory

-0.1MiB live, 160.7MiB allocated

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	890	15	905
Fresh	4	2	6
Picked	3	2	5
Done	0	1	1
Total	897	20	917

Accuracy

100.0%

Counts

917 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (*.f64 (+.f64 (cos.f64 (+.f64 x (+.f64 x eps))) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 1/2 binary64)))
✓	99.7%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.7%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (.f64 eps (sin.f64 x))))))
✓	99.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.7%	(.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)))
	99.7%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 (/.f64 (tan.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps eps) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))))
▶	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	98.1%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) (fma.f64 eps x #s(literal 1 binary64)))))
	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
▶	98.1%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64))))
	98.6%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2)))) (fma.f64 x (*.f64 eps (+.f64 eps x)) eps)))
▶	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 x eps))))) eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (*.f64 x x))) eps))
	54.5%	#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (.f64 eps (.f64 #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))))) (fma.f64 eps #s(approx (+ ( eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (neg.f64 eps))) (/.f64 (.f64 eps eps) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (neg.f64 eps)))))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) eps))))

Compiler

Compiled 873 to 401 computations (54.1% saved)

simplify345.0ms (2.3%)

Memory

-17.5MiB live, 541.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
cost-diff	0	(/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))))
cost-diff	0	(cos.f64 x)
cost-diff	0	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x))))
cost-diff	0	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps))
cost-diff	0	#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64)))
cost-diff	0	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
cost-diff	192	(+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
cost-diff	5824	(fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	6784	(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))

Rules

13 838×	`lower-fma.f32`
13 820×	`lower-fma.f64`
4 330×	`lower-*.f32`
4 318×	`lower-*.f64`
2 692×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	965
0	143	958
1	342	922
2	1228	827
3	5334	821
0	8194	805

Stop Event

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

Calls

Call 1

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

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

localize324.0ms (2.2%)

Memory

18.8MiB live, 393.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0.14343639836813848	#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))))
accuracy	0.18359375	(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.01171875	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.4745618093409555	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.015625	(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
accuracy	0.1171875	(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps))
accuracy	1.2060271157130906	#s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x))))
accuracy	0.00390625	(.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64)))
accuracy	0.21072892870839285	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64))))
accuracy	1.1812900739692078	#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64))
accuracy	0.03648378907376807	(pow.f64 (tan.f64 x) #s(literal 4 binary64))
accuracy	0.109375	(fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
accuracy	0.96875	(+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))

Samples

112.0ms	81×	1	valid
99.0ms	172×	0	valid
4.0ms	2×	2	valid
3.0ms	1×	3	valid

Compiler

Compiled 668 to 82 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

ival-add: 52.0ms (28.2% of total)

ival-mult: 44.0ms (23.9% of total)

const: 16.0ms (8.7% of total)

ival-div: 16.0ms (8.7% of total)

adjust: 15.0ms (8.1% of total)

ival-pow: 10.0ms (5.4% of total)

ival-pow2: 9.0ms (4.9% of total)

ival-cos: 7.0ms (3.8% of total)

ival-sin: 6.0ms (3.3% of total)

ival-tan: 5.0ms (2.7% of total)

ival-sub: 3.0ms (1.6% of total)

exact: 1.0ms (0.5% of total)

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

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

series36.0ms (0.2%)

Memory

-28.6MiB live, 54.5MiB allocated

Counts

24 → 504

Calls

Call 1

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

Outputs
#<alt x>
#<alt (* x (+ 1 (* 4/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 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) 4) (pow (cos x) 4))))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 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) 4) (pow (cos x) 4))))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))>
#<alt (* 1/3 (pow eps 2))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps x))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt 1/3>
#<alt (+ 1/3 (pow x 2))>
#<alt (+ 1/3 (* (pow x 2) (+ 1 (* 5/3 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ eps (pow (cos x) 2))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ eps (pow (cos x) 2))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (/ (* (pow eps 2) (sin x)) (pow (cos x) 3))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (/ (* (pow eps 2) (sin x)) (pow (cos x) 3))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt eps>
#<alt (+ eps (* (pow eps 2) x))>
#<alt (+ eps (* x (+ (* eps x) (pow eps 2))))>
#<alt (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* -1/6 eps) (* -3/2 eps)))))) (pow eps 2))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (/ 1 (pow (cos x) 2))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (/ (* eps (sin x)) (pow (cos x) 3))>
#<alt (* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))>
#<alt (/ (* eps (sin x)) (pow (cos x) 3))>
#<alt (* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))>
#<alt 1>
#<alt (+ 1 (* eps x))>
#<alt (+ 1 (* x (+ eps x)))>
#<alt (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* -1/6 eps) (* -3/2 eps))))))))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (* 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)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))>
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#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ eps (pow (cos x) 2))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (cos eps) (sin eps))>
#<alt (+ (* -1 x) (/ (cos eps) (sin eps)))>
#<alt (+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))>
#<alt (+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin eps)))>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))>
#<alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))>
#<alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))>
#<alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))>
#<alt (/ (pow (cos x) 2) eps)>
#<alt (/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)>
#<alt (/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)>
#<alt (/ (+ (* 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)>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (+ eps x))) (sin eps))>
#<alt (/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))>
#<alt (/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))>
#<alt (/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))>
#<alt (/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))>
#<alt (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (* (cos x) (cos (- eps (* -1 x))))>
#<alt (pow (cos x) 2)>
#<alt (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))>
#<alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (+ eps x)))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (* (cos x) (cos (- x (* -1 eps))))>
#<alt (pow x 4)>
#<alt (* (pow x 4) (+ 1 (* 4/3 (pow x 2))))>
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))>
#<alt (* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (/ (pow (sin x) 4) (pow (cos x) 4))>
#<alt (pow x 2)>
#<alt (+ (* eps x) (pow x 2))>
#<alt (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))>
#<alt (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))>
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))>
#<alt (* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))>
#<alt (* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))>
#<alt (* 1/3 (pow eps 2))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps x))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))>
#<alt (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))>
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))>
#<alt (* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))>
#<alt (* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))>
#<alt (* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))>
#<alt (* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))>
#<alt x>
#<alt (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))>
#<alt (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))>
#<alt (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))>
#<alt (* eps (+ 1/3 (* 4/3 (pow x 2))))>
#<alt (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))>
#<alt (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))>
#<alt (* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))>
#<alt (* eps (+ 1/3 (* 4/3 (pow x 2))))>
#<alt (* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))>
#<alt (* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))>
#<alt (* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))>
#<alt (* 1/3 eps)>
#<alt (+ x (* 1/3 eps))>
#<alt (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))>
#<alt (+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))>
#<alt (* 4/3 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* 4/3 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* 1/3 (/ eps (pow x 2))) (+ (* 4/3 eps) (/ 1 x))))>
#<alt (* (pow x 2) (+ (* 1/3 (/ eps (pow x 2))) (+ (* 4/3 eps) (/ 1 x))))>
#<alt (* 4/3 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* 4/3 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/3 (/ eps x)) 1) x)) (* 4/3 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1/3 (/ eps x)) 1) x)) (* 4/3 eps)))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>

Calls

126 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(+ (* eps (+ (* eps (+ (* (pow (tan x) 2) 1/3) (+ 1/2 (+ -1/6 (+ (pow (tan x) 2) (pow (tan x) 4)))))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
2.0ms	x	@	-inf	(+ (* eps (+ (* eps (+ (* (pow (tan x) 2) 1/3) (+ 1/2 (+ -1/6 (+ (pow (tan x) 2) (pow (tan x) 4)))))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
2.0ms	x	@	0	(/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))
1.0ms	eps	@	0	(+ (* eps (+ (* eps (+ (* (pow (tan x) 2) 1/3) (+ 1/2 (+ -1/6 (+ (pow (tan x) 2) (pow (tan x) 4)))))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
1.0ms	eps	@	-inf	(+ (* eps (+ (* eps (+ (* (pow (tan x) 2) 1/3) (+ 1/2 (+ -1/6 (+ (pow (tan x) 2) (pow (tan x) 4)))))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))

simplify365.0ms (2.5%)

Memory

17.9MiB live, 452.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 262×	`lower-fma.f64`
7 262×	`lower-fma.f32`
5 130×	`lower-*.f64`
5 130×	`lower-*.f32`
4 226×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	622	10555
1	2656	10417
0	8398	9931

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 499

Calls

Call 1

Inputs
x
(* x (+ 1 (* 4/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 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) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 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) 4) (pow (cos x) 4))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(* 1/3 (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 (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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1/3
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eps
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1
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(/ (sin eps) (cos eps))
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(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))))))))
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(+ eps (* 1/3 (pow eps 3)))
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(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
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(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
eps
(+ eps (* eps (pow x 2)))
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(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
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1
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(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
1
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(cos x)
(cos x)
(cos x)
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(cos x)
(cos x)
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(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(pow x 4)
(* (pow x 4) (+ 1 (* 4/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
x
(+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))
(+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))
(+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))
(* eps (+ 1/3 (* 4/3 (pow x 2))))
(* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* eps (+ 1/3 (* 4/3 (pow x 2))))
(* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))
(* 1/3 eps)
(+ x (* 1/3 eps))
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (/ 1 x)))
(* (pow x 2) (+ (* 1/3 (/ eps (pow x 2))) (+ (* 4/3 eps) (/ 1 x))))
(* (pow x 2) (+ (* 1/3 (/ eps (pow x 2))) (+ (* 4/3 eps) (/ 1 x))))
(* 4/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 4/3 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/3 (/ eps x)) 1) x)) (* 4/3 eps)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/3 (/ eps x)) 1) x)) (* 4/3 eps)))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* 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))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 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))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 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))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))

Outputs
x
(* x (+ 1 (* 4/3 (pow x 2))))
(fma.f64 x (.f64 #s(literal 4/3 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/15 binary64) #s(literal 4/3 binary64)) #s(literal 1 binary64)))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 248/315 binary64) #s(literal 17/15 binary64)) #s(literal 4/3 binary64))) x)
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/ (pow (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) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 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 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 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 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(.f64 (+.f64 #s(literal 1/3 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 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 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) 4) (pow (cos x) 4))))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 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) 4) (pow (cos x) 4))))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))
(.f64 (+.f64 #s(literal 1/3 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 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))) eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (+.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))) eps))))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
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1/3
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eps
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(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(.f64 eps (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(.f64 eps (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))
(* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))
(.f64 eps (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))
(/ (* eps (sin x)) (pow (cos x) 3))
(/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(.f64 (neg.f64 eps) (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(.f64 (neg.f64 eps) (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))
(* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))
(.f64 (neg.f64 eps) (+.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))
1
#s(literal 1 binary64)
(+ 1 (* eps x))
(fma.f64 x eps #s(literal 1 binary64))
(+ 1 (* x (+ eps x)))
(fma.f64 x (+.f64 x eps) #s(literal 1 binary64))
(+ 1 (* x (+ eps (* x (+ 1 (* x (- (* -1/6 eps) (* -3/2 eps))))))))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 #s(literal 4/3 binary64) eps) #s(literal 1 binary64)) eps) #s(literal 1 binary64))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 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 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (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 x (fma.f64 x (/.f64 (*.f64 (sin.f64 eps) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.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 x (fma.f64 x (fma.f64 x (neg.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (+.f64 #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 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 eps) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.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)))
(- (/ (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)))
(- (/ (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)))
(- (/ (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)))
(* 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 eps (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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)))))
(+.f64 eps (.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal -1/6 binary64) (neg.f64 (-.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+.f64 eps (.f64 (fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 x) (/.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (/.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)))) (neg.f64 eps) #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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.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)))) (/ (sin x) (cos x)))
(-.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)))) (/ (sin x) (cos x)))
(-.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)))) (/ (sin x) (cos x)))
(-.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)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* 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) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/6 binary64) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.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 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/6 binary64) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.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 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
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(* (pow eps 3) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(+ (* eps (+ (* eps (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))))
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(* 1/3 (pow eps 2))
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(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
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(fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) eps) (.f64 (sin.f64 x) (cos.f64 x)))) (.f64 (cos.f64 x) (neg.f64 (sin.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (+ 1 (* 4/3 (pow x 2))))
(.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 6/5 binary64) #s(literal 4/3 binary64)) #s(literal 1 binary64)))
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2))))))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 848/945 binary64) #s(literal 6/5 binary64)) #s(literal 4/3 binary64)) #s(literal 1 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(pow x 2)
(*.f64 x x)
(+ (* eps x) (pow x 2))
(*.f64 x (+.f64 x eps))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) (.f64 x x))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 x eps)))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (+.f64 (/.f64 x eps) (/.f64 (.f64 x x) (*.f64 eps eps)))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (+.f64 (/.f64 x eps) (/.f64 (.f64 x x) (*.f64 eps eps)))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 x eps)))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) (/.f64 (+.f64 x (/.f64 (.f64 x x) eps)) eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) (/.f64 (+.f64 x (/.f64 (.f64 x x) eps)) eps))))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(.f64 (.f64 x x) (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (/.f64 eps x)))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (/.f64 eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (/.f64 eps x)))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(.f64 (.f64 x x) (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (/.f64 eps x)))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) x) eps) x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) x) eps) x))))
x
(+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* eps (+ 1/3 (* 4/3 (pow x 2))))
(.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(.f64 eps (+.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (/.f64 x eps)))
(* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(.f64 eps (+.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (/.f64 x eps)))
(* eps (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(.f64 eps (+.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) (/.f64 x eps)))
(* eps (+ 1/3 (* 4/3 (pow x 2))))
(.f64 eps (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))
(.f64 (neg.f64 eps) (-.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64)) (/.f64 x eps)))
(* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))
(.f64 (neg.f64 eps) (-.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64)) (/.f64 x eps)))
(* -1 (* eps (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps)))))
(.f64 (neg.f64 eps) (-.f64 (fma.f64 (.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64)) (/.f64 x eps)))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(+ x (* 1/3 eps))
(fma.f64 eps #s(literal 1/3 binary64) x)
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 4/3 binary64) eps) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))
(+ (* 1/3 eps) (* x (+ 1 (* 4/3 (* eps x)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 4/3 binary64) eps) #s(literal 1 binary64)) (.f64 eps #s(literal 1/3 binary64)))
(* 4/3 (* eps (pow x 2)))
(.f64 #s(literal 4/3 binary64) (.f64 (*.f64 x x) eps))
(* (pow x 2) (+ (* 4/3 eps) (/ 1 x)))
(.f64 (.f64 x x) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x)))
(* (pow x 2) (+ (* 1/3 (/ eps (pow x 2))) (+ (* 4/3 eps) (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (/.f64 eps (*.f64 x x)) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x))))
(* (pow x 2) (+ (* 1/3 (/ eps (pow x 2))) (+ (* 4/3 eps) (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (/.f64 eps (*.f64 x x)) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x))))
(* 4/3 (* eps (pow x 2)))
(.f64 #s(literal 4/3 binary64) (.f64 (*.f64 x x) eps))
(* (pow x 2) (+ (* 4/3 eps) (/ 1 x)))
(.f64 (.f64 x x) (fma.f64 #s(literal 4/3 binary64) eps (/.f64 #s(literal 1 binary64) x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/3 (/ eps x)) 1) x)) (* 4/3 eps)))
(.f64 (.f64 x x) (-.f64 (*.f64 #s(literal 4/3 binary64) eps) (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/3 binary64) #s(literal -1 binary64)) x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1/3 (/ eps x)) 1) x)) (* 4/3 eps)))
(.f64 (.f64 x x) (-.f64 (*.f64 #s(literal 4/3 binary64) eps) (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/3 binary64) #s(literal -1 binary64)) x)))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(sin (neg (* -1 eps)))
(sin.f64 eps)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x (sin.f64 eps)) (.f64 (cos.f64 eps) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 eps))) (cos.f64 eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 eps (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (neg.f64 (sin.f64 x))) (cos.f64 x))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))

rewrite409.0ms (2.8%)

Memory

34.9MiB live, 499.1MiB allocated

Rules

5 072×	`lower-fma.f32`
5 054×	`lower-fma.f64`
3 990×	`lower-*.f32`
3 978×	`lower-*.f64`
2 738×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	747
0	143	717
1	735	529
2	7682	529
0	8016	511

Stop Event

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

Counts

24 → 399

Calls

Call 1

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

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

eval149.0ms (1%)

Memory: -18.1MiB live, 265.2MiB allocated
Compiler: Compiled 37 079 to 2 511 computations (93.2% saved)

prune143.0ms (1%)

Memory

-19.9MiB live, 184.0MiB allocated

Pruning

24 alts after pruning (19 fresh and 5 done)

	Pruned	Kept	Total
New	999	13	1 012
Fresh	6	6	12
Picked	3	2	5
Done	0	3	3
Total	1 008	24	1 032

Accuracy

100.0%

Counts

1 032 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.7%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (.f64 eps (sin.f64 x))))))
✓	99.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))))
	98.5%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))))
	98.3%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.7%	(.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)))
	99.7%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 (/.f64 (tan.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps eps) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))))
	99.3%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
	98.6%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
	98.7%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
	99.3%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) eps))
	98.1%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) (fma.f64 x eps #s(literal 1 binary64)))))
✓	98.1%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (.f64 eps #s(approx (+ ( eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))) #s(literal 1 binary64))))
	98.6%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)))
	98.5%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
	98.6%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (/ 1 (pow (cos x) 2)))) (fma.f64 x (*.f64 eps (+.f64 eps x)) eps)))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps #s(approx (+ (* eps (+ (* 4/3 (* x x)) 1/3)) x) (fma.f64 eps #s(literal 1/3 binary64) x)) (*.f64 x x)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* 4/3 (* eps eps)) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (/.f64 x eps))))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/6) (+ (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) 1/2)) (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6))) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (sin x) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/3 binary64))) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) eps))))

Compiler

Compiled 1 664 to 491 computations (70.5% saved)

regimes51.0ms (0.3%)

Memory

7.5MiB live, 82.0MiB allocated

Counts

59 → 1

Calls

Call 1

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

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

Calls

3 calls:

17.0ms	x
17.0ms	eps
14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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 15 to 10 computations (33.3% saved)

regimes32.0ms (0.2%)

Memory

25.9MiB live, 63.0MiB allocated

Counts

37 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Memory

-42.9MiB live, 51.2MiB allocated

Counts

33 → 1

Calls

Call 1

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

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

Calls

3 calls:

13.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

4.6MiB live, 43.7MiB allocated

Counts

31 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.2%)

Memory

8.7MiB live, 47.0MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

9.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

-6.4MiB live, 32.9MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

22.0MiB live, 22.0MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-27.9MiB live, 15.5MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

-32.3MiB live, 6.8MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms	eps
1.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify15.0ms (0.1%)

Memory

21.5MiB live, 21.5MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`unsub-neg_binary64`
32×	`*-commutative_binary64`
32×	`distribute-lft-neg-in_binary64`
28×	`cancel-sub-sign_binary64`
26×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	115	537
1	133	537
2	145	537
3	166	537
4	187	537
5	217	537
6	241	537
7	258	537
8	268	537
9	276	537

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (8.4%)

Memory

-6.0MiB live, 1 110.7MiB allocated

Rules

11 644×	`lower-fma.f64`
11 644×	`lower-fma.f32`
9 672×	`lower-fma.f64`
9 672×	`lower-fma.f32`
7 262×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1399
1	548	1330
2	2246	1322
0	8168	1258
0	92	747
0	143	717
1	735	529
2	7682	529
0	8016	511
0	6	16
0	10	16
1	52	16
2	446	16
3	6895	16
0	8417	16
0	680	11088
1	2760	10914
0	8567	10532
0	67	773
0	99	749
1	514	505
2	4952	493
0	8152	472
0	491	11125
1	2052	10047
0	8361	9548
0	622	10555
1	2656	10417
0	8398	9931

Stop Event

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

Compiler

Compiled 644 to 317 computations (50.8% saved)

preprocess85.0ms (0.6%)

Memory: 17.9MiB live, 173.6MiB allocated
Compiler: Compiled 424 to 150 computations (64.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	42	35
2	112	35
3	270	35
4	462	35
5	516	35
6	539	35
7	546	35
0	6	7
0	10	7
1	15	7
2	28	7
3	56	7
4	114	7
5	191	7
6	228	7
7	235	7
0	235	7

Iter	Nodes	Cost
0	115	537
1	133	537
2	145	537
3	166	537
4	187	537
5	217	537
6	241	537
7	258	537
8	268	537
9	276	537

Iter	Nodes	Cost
0	18	39
1	42	35
2	112	35
3	270	35
4	462	35
5	516	35
6	539	35
7	546	35
0	6	7
0	10	7
1	15	7
2	28	7
3	56	7
4	114	7
5	191	7
6	228	7
7	235	7
0	235	7

Iter	Nodes	Cost
0	115	537
1	133	537
2	145	537
3	166	537
4	187	537
5	217	537
6	241	537
7	258	537
8	268	537
9	276	537

start0.0ms (0%)

analyze64.0ms (0.4%)

sample5.9s (39.9%)

explain126.0ms (0.9%)

preprocess40.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize93.0ms (0.6%)

series11.0ms (0.1%)

simplify867.0ms (5.9%)

rewrite273.0ms (1.9%)

eval50.0ms (0.3%)

prune67.0ms (0.5%)

simplify429.0ms (2.9%)

localize259.0ms (1.8%)

series92.0ms (0.6%)

simplify373.0ms (2.5%)

rewrite550.0ms (3.7%)

eval433.0ms (2.9%)

prune203.0ms (1.4%)

simplify348.0ms (2.4%)

localize252.0ms (1.7%)

series28.0ms (0.2%)

simplify371.0ms (2.5%)

rewrite330.0ms (2.2%)

eval110.0ms (0.7%)

prune82.0ms (0.6%)

simplify345.0ms (2.3%)

localize324.0ms (2.2%)

series36.0ms (0.2%)

simplify365.0ms (2.5%)

rewrite409.0ms (2.8%)

eval149.0ms (1%)

prune143.0ms (1%)

regimes51.0ms (0.3%)

regimes32.0ms (0.2%)

regimes33.0ms (0.2%)

regimes27.0ms (0.2%)

regimes26.0ms (0.2%)

regimes18.0ms (0.1%)

regimes16.0ms (0.1%)

regimes13.0ms (0.1%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes7.0ms (0%)

regimes7.0ms (0.1%)

simplify15.0ms (0.1%)

soundness1.2s (8.4%)

preprocess85.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	42	35
2	112	35
3	270	35
4	462	35
5	516	35
6	539	35
7	546	35
0	6	7
0	10	7
1	15	7
2	28	7
3	56	7
4	114	7
5	191	7
6	228	7
7	235	7
0	235	7

Iter	Nodes	Cost
0	115	537
1	133	537
2	145	537
3	166	537
4	187	537
5	217	537
6	241	537
7	258	537
8	268	537
9	276	537