Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze41.0ms (0.3%)

Memory

-3.2MiB live, 53.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.6s (48.9%)

Memory

-151.7MiB live, 7 900.9MiB allocated

Samples

3.6s	26 447×	0	invalid
812.0ms	2 831×	1	valid
750.0ms	5 425×	0	valid

Precisions

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

const: 838.0ms (22% of total)

ival-tan: 817.0ms (21.5% of total)

ival-add: 536.0ms (14.1% of total)

ival-mult: 359.0ms (9.4% of total)

ival-<=: 269.0ms (7.1% of total)

ival-sub: 254.0ms (6.7% of total)

ival-fabs: 248.0ms (6.5% of total)

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

ival-and: 102.0ms (2.7% of total)

adjust: 83.0ms (2.2% of total)

exact: 45.0ms (1.2% of total)

ival-assert: 13.0ms (0.3% of total)

Bogosity

explain111.0ms (0.8%)

Memory

6.8MiB live, 168.1MiB 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

22.0ms	6×	3	valid
19.0ms	342×	0	valid
17.0ms	162×	1	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: 44.0ms

ival-tan: 33.0ms (75.7% of total)

adjust: 4.0ms (9.2% of total)

ival-add: 3.0ms (6.9% of total)

ival-sub: 3.0ms (6.9% of total)

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

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

preprocess27.0ms (0.2%)

Memory

-20.8MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

simplify7.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB 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

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
36×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize36.0ms (0.3%)

Memory

26.0MiB live, 26.0MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

12.0ms	3×	3	valid
9.0ms	171×	0	valid
9.0ms	81×	1	valid
1.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-tan: 17.0ms (74.1% of total)

adjust: 2.0ms (8.7% of total)

ival-add: 2.0ms (8.7% of total)

ival-sub: 2.0ms (8.7% of total)

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

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

series38.0ms (0.3%)

Memory

-27.1MiB live, 10.9MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(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))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(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))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(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))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(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))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
3.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify200.0ms (1.5%)

Memory

33.3MiB live, 108.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
5 316×	`lower-*.f64`
5 316×	`lower-*.f32`
2 664×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1351
1	464	1285
2	1534	1274
3	5964	1242
0	8538	1195

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite255.0ms (1.9%)

Memory

-43.6MiB live, 125.3MiB allocated

Rules

4 404×	`lower-*.f64`
4 404×	`lower-*.f32`
3 318×	`lower-/.f64`
3 318×	`lower-/.f32`
3 264×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 259

Calls

Call 1

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

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

eval55.0ms (0.4%)

Memory: 11.9MiB live, 49.0MiB allocated
Compiler: Compiled 8 701 to 985 computations (88.7% saved)

prune186.0ms (1.4%)

Memory

-5.6MiB live, 76.6MiB allocated

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	320	16	336
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	320	17	337

Accuracy

100.0%

Counts

337 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.7%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
	62.5%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
	61.5%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
	62.5%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	62.5%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
	62.6%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	62.5%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
▶	62.6%	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (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) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
▶	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 751 to 382 computations (49.1% saved)

simplify163.0ms (1.2%)

Memory

32.1MiB live, 105.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (tan.f64 eps) (tan.f64 x))
cost-diff	0	(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))))
cost-diff	0	(.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)))
cost-diff	0	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
cost-diff	0	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))
cost-diff	384	(-.f64 (+.f64 eps x) x)
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
cost-diff	0	(/.f64 (sin.f64 x) (cos.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)) (/.f64 (sin.f64 x) (cos.f64 x)))
cost-diff	0	#s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) 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) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	26816	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))

Rules

13 846×	`lower-fma.f32`
13 832×	`lower-fma.f64`
3 918×	`lower-*.f32`
3 908×	`lower-*.f64`
2 730×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	778
0	113	774
1	187	698
2	407	680
3	1157	677
4	4729	677
0	8416	667

Stop Event

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

Calls

Call 1

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

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

localize290.0ms (2.2%)

Memory

-21.5MiB live, 409.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (tan.f64 eps) (tan.f64 x))
accuracy	0.01953125	(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy	0.10775375976844201	(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
accuracy	23.918482892439503	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
accuracy	0.015625	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.05097464160568397	(cos.f64 (+.f64 eps x))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
accuracy	23.96972852167959	(-.f64 (+.f64 eps x) x)
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(/.f64 (sin.f64 x) (cos.f64 x))
accuracy	0.07219329735525833	(tan.f64 (+.f64 x eps))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy	0.0078125	(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
accuracy	0.07219329735525833	(tan.f64 (+.f64 x eps))
accuracy	0.9033645080441755	#s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
accuracy	0.033535009768442016	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.109375	(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.9889450195368841	(-.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 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

114.0ms	88×	1	valid
85.0ms	162×	0	valid
21.0ms	4×	3	valid
6.0ms	2×	2	valid

Compiler

Compiled 709 to 63 computations (91.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 187.0ms

adjust: 34.0ms (18.2% of total)

ival-mult: 28.0ms (15% of total)

ival-tan: 22.0ms (11.8% of total)

ival-div: 21.0ms (11.2% of total)

ival-pow: 21.0ms (11.2% of total)

ival-add: 20.0ms (10.7% of total)

ival-sub: 11.0ms (5.9% of total)

const: 10.0ms (5.4% of total)

ival-pow2: 10.0ms (5.4% of total)

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

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

exact: 1.0ms (0.5% of total)

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

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

series99.0ms (0.7%)

Memory

27.2MiB live, 183.7MiB allocated

Counts

25 → 516

Calls

Call 1

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

Outputs
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())) ())
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#s(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))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())) ())
#s(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))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
20.0ms	x	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (tan x)) (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (+ (* (* x x) 1/3) 1) (cos x) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
15.0ms	x	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (tan x)) (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (+ (* (* x x) 1/3) 1) (cos x) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
13.0ms	eps	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (tan x)) (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (+ (* (* x x) 1/3) 1) (cos x) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
9.0ms	eps	@	0	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (tan x)) (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (+ (* (* x x) 1/3) 1) (cos x) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))
8.0ms	eps	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (- (+ eps x) x) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (tan x)) (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 3) (+ (* (* x x) 1/3) 1) (cos x) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x)))

simplify216.0ms (1.6%)

Memory

17.1MiB live, 241.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 218×	`lower-fma.f64`
13 218×	`lower-fma.f32`
7 794×	`lower-*.f64`
7 794×	`lower-*.f32`
4 272×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	709	11463
1	2285	11197
2	7608	11093
0	8838	10702

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 484

Calls

Call 1

Inputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- 1 (* -1 (/ (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 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)))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
eps
eps
eps
eps
(/ (pow (cos x) 2) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
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(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (sin x) (cos x)))
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(+ (* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x)))
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(/ (sin x) (cos x))
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(/ (pow (sin x) 2) (pow (cos x) 2))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(cos x)
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(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos 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 x))))
eps
eps
eps
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))
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(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
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(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
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(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
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eps
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eps
eps
eps
eps
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
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(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps))))
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(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(+ (/ (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)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(cos x)
(cos x)
(cos x)
(cos x)
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (- eps (* -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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (- eps (* -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)))
(/ (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))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos 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)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos 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
eps
eps
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)))) (sin eps))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(+ (/ (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)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(cos x)
(cos x)
(cos x)
(cos x)
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))

Outputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* 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 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (-.f64 #s(literal 1/6 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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cos.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)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* 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 (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (neg.f64 (fma.f64 (fma.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/3 binary64) (.f64 (+.f64 (-.f64 #s(literal 1/6 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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (+.f64 (-.f64 #s(literal 1/6 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)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) eps)) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
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x
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eps
eps
eps
eps
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (sin x) (cos x)))
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(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ eps (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x)))
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(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (fma.f64 (+.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)))) eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) eps #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ eps (/ (sin x) (cos x)))
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(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x)))
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(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(cos x)
(cos.f64 x)
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(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(.f64 (.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(/ (* eps (sin x)) (cos x))
(*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(.f64 (fma.f64 (/.f64 (.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x)) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps)
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 2/15 binary64) (.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps)
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 17/315 binary64) (.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal 2/15 binary64)) (cos.f64 x))) (.f64 eps eps) (/.f64 (.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) 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)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 (*.f64 eps eps) eps) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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))) #s(literal 1/3 binary64))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 (.f64 eps eps) eps))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/3 binary64)) (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) eps)) (+.f64 (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (.f64 (*.f64 eps eps) eps))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(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))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
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(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
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(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
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(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
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(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
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(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))))
-1/2
#s(literal -1/2 binary64)
(- (* -1/3 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(fma.f64 (fma.f64 #s(literal -2/9 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -17/135 binary64) (.f64 x x) #s(literal -2/9 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
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(+ eps (* 1/3 (pow eps 3)))
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(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
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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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(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
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(/ (sin eps) (cos eps))
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eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
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x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
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(/ (sin eps) (cos eps))
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eps
eps
eps
eps
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64)) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x)))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64)) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x)))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64)) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x)))
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64)) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x)))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) #s(literal 1 binary64))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(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))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(.f64 (sin.f64 eps) (/.f64 (sin.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))))

rewrite231.0ms (1.7%)

Memory

1.9MiB live, 244.8MiB allocated

Rules

5 004×	`lower-*.f32`
4 994×	`lower-*.f64`
4 976×	`lower-fma.f32`
4 962×	`lower-fma.f64`
2 392×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	487
0	113	472
1	505	369
2	4635	369
0	8175	353

Stop Event

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

Counts

25 → 692

Calls

Call 1

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

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

eval250.0ms (1.9%)

Memory: 19.4MiB live, 362.6MiB allocated
Compiler: Compiled 60 779 to 3 997 computations (93.4% saved)

prune172.0ms (1.3%)

Memory

-33.9MiB live, 261.0MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	1 419	12	1 431
Fresh	11	0	11
Picked	5	0	5
Done	0	1	1
Total	1 435	13	1 448

Accuracy

100.0%

Counts

1 448 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 #s(literal 0 binary64) eps))))))
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
▶	99.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.9%	(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
▶	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
	99.9%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
▶	99.2%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (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 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))

Compiler

Compiled 527 to 290 computations (45% saved)

simplify156.0ms (1.2%)

Memory

23.3MiB live, 141.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))
cost-diff	0	#s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
cost-diff	0	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
cost-diff	0	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))

Rules

12 094×	`lower-fma.f32`
12 084×	`lower-fma.f64`
3 570×	`lower-*.f32`
3 560×	`lower-*.f64`
2 900×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	782
0	106	776
1	183	688
2	446	676
3	1543	676
4	3898	676
0	8188	658

Stop Event

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

Calls

Call 1

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

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

localize211.0ms (1.6%)

Memory

14.0MiB live, 247.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 (cos.f64 x) (sin.f64 eps))
accuracy	0.01171875	(*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.13671875	(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	1.2060271157130906	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
accuracy	0.00390625	(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	31.424916395330225	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.01171875	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.015625	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.05097464160568397	(cos.f64 (+.f64 eps x))

Samples

84.0ms	171×	0	valid
75.0ms	81×	1	valid
4.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 532 to 67 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 132.0ms

ival-mult: 23.0ms (17.4% of total)

ival-div: 19.0ms (14.4% of total)

adjust: 18.0ms (13.6% of total)

ival-add: 17.0ms (12.8% of total)

ival-pow: 14.0ms (10.6% of total)

const: 12.0ms (9.1% of total)

ival-cos: 7.0ms (5.3% of total)

ival-sin: 7.0ms (5.3% of total)

ival-pow2: 6.0ms (4.5% of total)

ival-sub: 5.0ms (3.8% of total)

ival-tan: 4.0ms (3% of total)

exact: 1.0ms (0.8% of total)

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

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

series65.0ms (0.5%)

Memory

-9.8MiB live, 73.0MiB allocated

Counts

22 → 480

Calls

Call 1

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

Outputs
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) (patch (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) (patch (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) (patch (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) (patch (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow (cos x) 2)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (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 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(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)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) #<representation binary64>) () ())) ())
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#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt (/.f64 (cos.f64 x) (sin.f64 eps)) (patch (/.f64 (cos.f64 x) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt (/.f64 (cos.f64 x) (sin.f64 eps)) (patch (/.f64 (cos.f64 x) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt (/.f64 (cos.f64 x) (sin.f64 eps)) (patch (/.f64 (cos.f64 x) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt (/.f64 (cos.f64 x) (sin.f64 eps)) (patch (/.f64 (cos.f64 x) (sin.f64 eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	inf	((* (/ 1 (* (cos (+ eps x)) (cos x))) (sin (+ 0 eps))) (+ 0 eps) (/ 1 (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (cos (+ eps x)) (/ (cos x) (sin eps)))
6.0ms	x	@	-inf	((* (/ 1 (* (cos (+ eps x)) (cos x))) (sin (+ 0 eps))) (+ 0 eps) (/ 1 (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (cos (+ eps x)) (/ (cos x) (sin eps)))
6.0ms	x	@	inf	((* (/ 1 (* (cos (+ eps x)) (cos x))) (sin (+ 0 eps))) (+ 0 eps) (/ 1 (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (cos (+ eps x)) (/ (cos x) (sin eps)))
5.0ms	eps	@	-inf	((* (/ 1 (* (cos (+ eps x)) (cos x))) (sin (+ 0 eps))) (+ 0 eps) (/ 1 (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (cos (+ eps x)) (/ (cos x) (sin eps)))
4.0ms	eps	@	0	((* (/ 1 (* (cos (+ eps x)) (cos x))) (sin (+ 0 eps))) (+ 0 eps) (/ 1 (* (cos (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (cos (+ eps x)) (/ (cos x) (sin eps)))

simplify243.0ms (1.8%)

Memory

-48.3MiB live, 181.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 350×	`lower-fma.f64`
11 350×	`lower-fma.f32`
6 196×	`lower-*.f64`
6 196×	`lower-*.f32`
4 476×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	580	10406
1	1818	10139
2	6122	9942
0	8323	9547

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 467

Calls

Call 1

Inputs
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
eps
eps
eps
eps
(/ 1 (pow (cos x) 2))
(+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (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 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(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))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (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 (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (pow (cos x) 2) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (pow (cos x) 2) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(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 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 x) eps)
(/ (+ (cos x) (* 1/6 (* (pow eps 2) (cos x)))) eps)
(/ (+ (cos x) (* (pow eps 2) (- (* -1 (* (pow eps 2) (+ (* -1/36 (cos x)) (* 1/120 (cos x))))) (* -1/6 (cos x))))) eps)
(/ (+ (cos x) (* (pow eps 2) (- (* (pow eps 2) (- (* -1 (* (pow eps 2) (+ (* -1/5040 (cos x)) (+ (* 1/720 (cos x)) (* 1/6 (+ (* -1/36 (cos x)) (* 1/120 (cos x)))))))) (+ (* -1/36 (cos x)) (* 1/120 (cos x))))) (* -1/6 (cos x))))) 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))))
eps
eps
eps
eps
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(/ 1 (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps 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 x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 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)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (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))))))
(/ (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))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (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))))
(/ (* (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 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 (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin 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 (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
eps
eps
eps
eps
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(/ 1 (* (cos x) (cos (- x (* -1 eps)))))
(* (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 (- 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)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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eps
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1
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1
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(- (/ (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)))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow 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)))))
(/ (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))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(cos x)
(cos x)
(cos x)
(cos 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 x))))
(/ (* (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 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 (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (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)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 x)))))
(/ 1 (* (cos x) (cos (- eps (* -1 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))))
(- (/ (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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(- (/ (sin (- eps (* -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 (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (pow 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)))))
(/ (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 (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(cos x)
(cos x)
(cos x)
(cos 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)))))
(/ (* (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)))) (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)))) (sin eps))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))

Outputs
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(fma.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 eps eps) (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (.f64 eps eps) (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
eps
eps
eps
eps
(/ 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 (sin.f64 x) (/.f64 eps (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 (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))))) (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 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (- 1 (* -1 (/ (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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(/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
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(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
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(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
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(/ (pow (cos x) 2) eps)
(/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
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(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
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(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
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(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
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(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
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(/ (cos x) eps)
(/.f64 (cos.f64 x) eps)
(/ (+ (cos x) (* 1/6 (* (pow eps 2) (cos x)))) eps)
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x)) eps)
(/ (+ (cos x) (* (pow eps 2) (- (* -1 (* (pow eps 2) (+ (* -1/36 (cos x)) (* 1/120 (cos x))))) (* -1/6 (cos x))))) eps)
(/.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal 7/360 binary64)) (.f64 eps eps) (.f64 #s(literal 1/6 binary64) (cos.f64 x))) (.f64 eps eps) (cos.f64 x)) eps)
(/ (+ (cos x) (* (pow eps 2) (- (* (pow eps 2) (- (* -1 (* (pow eps 2) (+ (* -1/5040 (cos x)) (+ (* 1/720 (cos x)) (* 1/6 (+ (* -1/36 (cos x)) (* 1/120 (cos x)))))))) (+ (* -1/36 (cos x)) (* 1/120 (cos x))))) (* -1/6 (cos x))))) eps)
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(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
eps
eps
eps
eps
(/ 1 (* (cos x) (cos (+ eps x))))
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ 1 (* (cos x) (cos (+ eps x))))
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ 1 (* (cos x) (cos (+ eps x))))
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ 1 (* (cos x) (cos (+ eps x))))
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (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 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)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (+.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) #s(literal 1/3 binary64)) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 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 eps eps) eps))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* 1/3 (pow eps 2))
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(* 1/3 (pow eps 2))
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(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(- (/ (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)))
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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)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) (+.f64 (+.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) #s(literal 1/3 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (*.f64 eps eps))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
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(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
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(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(.f64 (+.f64 (fma.f64 x (/.f64 x (.f64 eps eps)) (/.f64 x eps)) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(.f64 (+.f64 (fma.f64 x (/.f64 x (.f64 eps eps)) (/.f64 x eps)) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) (.f64 eps eps))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
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(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (+ eps x))) (sin eps))
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(/ (* (cos x) (cos (+ eps x))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(cos (+ eps x))
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(cos (+ eps x))
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(cos (+ eps x))
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(cos (+ eps x))
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(cos (+ eps x))
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(cos (+ eps x))
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(cos (+ eps x))
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(/ (cos x) (sin eps))
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(/ (cos x) (sin eps))
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eps
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(fma.f64 (*.f64 x eps) x eps)
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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(cos eps)
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(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 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 (- 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) (sin eps))
(/.f64 (cos.f64 x) (sin.f64 eps))
(/ (cos x) (sin eps))
(/.f64 (cos.f64 x) (sin.f64 eps))
(/ (cos x) (sin eps))
(/.f64 (cos.f64 x) (sin.f64 eps))
(/ (cos x) (sin eps))
(/.f64 (cos.f64 x) (sin.f64 eps))

rewrite210.0ms (1.6%)

Memory

12.4MiB live, 246.7MiB allocated

Rules

4 844×	`lower-*.f32`
4 834×	`lower-*.f64`
4 500×	`lower-fma.f32`
4 490×	`lower-fma.f64`
2 250×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	723
0	106	719
1	506	548
2	4737	536
0	8169	506

Stop Event

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

Counts

22 → 446

Calls

Call 1

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

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

eval213.0ms (1.6%)

Memory: 25.4MiB live, 184.9MiB allocated
Compiler: Compiled 24 645 to 1 730 computations (93% saved)

prune175.0ms (1.3%)

Memory

-7.2MiB live, 199.5MiB allocated

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	957	20	977
Fresh	4	3	7
Picked	4	1	5
Done	0	1	1
Total	965	25	990

Accuracy

100.0%

Counts

990 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
▶	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.9%	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
	57.4%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (.f64 (.f64 (+.f64 (+.f64 x eps) x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x eps) x)))))
	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 eps))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
	34.9%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 eps eps))))
	55.2%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 eps))))
	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
▶	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	98.7%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
	98.1%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps 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))))) eps))
▶	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
▶	98.5%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps)))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (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 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps))))

Compiler

Compiled 911 to 482 computations (47.1% saved)

simplify176.0ms (1.3%)

Memory

-16.4MiB live, 93.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))
cost-diff	0	#s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
cost-diff	0	(fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)
cost-diff	0	(fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)
cost-diff	0	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))
cost-diff	0	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
cost-diff	0	(*.f64 x eps)
cost-diff	0	(fma.f64 (*.f64 x eps) x eps)
cost-diff	0	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps))
cost-diff	0	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps)))
cost-diff	0	(cos.f64 x)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (cos.f64 x))
cost-diff	704	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))

Rules

11 608×	`lower-fma.f32`
11 596×	`lower-fma.f64`
3 564×	`lower-+.f32`
3 562×	`lower-+.f64`
2 578×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	407
0	75	407
1	124	395
2	206	379
3	426	379
4	1250	379
5	4568	379
0	8105	369

Stop Event

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

Calls

Call 1

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

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

localize131.0ms (1%)

Memory

23.5MiB live, 175.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))))
accuracy	0.18172894020834907	#s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))
accuracy	0.01171875	(fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))
accuracy	0.015625	(fma.f64 #s(literal -2/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
accuracy	0.8285287041778722	#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.0078125	(fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)
accuracy	0.3125	(*.f64 #s(literal 2/3 binary64) eps)
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
accuracy	0.8186173525058796	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))
accuracy	0	(fma.f64 (*.f64 x eps) x eps)
accuracy	0	(*.f64 x eps)
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps)))
accuracy	0.9227288180468125	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps))
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
accuracy	0.01171875	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))

Samples

87.0ms	249×	0	valid
4.0ms	7×	1	valid

Compiler

Compiled 263 to 43 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 24.0ms (33.7% of total)

ival-div: 13.0ms (18.2% of total)

const: 9.0ms (12.6% of total)

ival-add: 9.0ms (12.6% of total)

ival-sin: 7.0ms (9.8% of total)

ival-cos: 5.0ms (7% of total)

ival-pow2: 2.0ms (2.8% of total)

adjust: 1.0ms (1.4% of total)

ival-sub: 1.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series68.0ms (0.5%)

Memory

5.3MiB live, 89.0MiB allocated

Counts

24 → 504

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) (patch (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 eps) (cos.f64 x)) (patch (/.f64 (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps))) #<representation binary64>) () ())
#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x eps) x eps) (patch (fma.f64 (.f64 x eps) x eps) #<representation binary64>) () ())
#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) (patch (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (patch (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (patch (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2/3 binary64) eps) (patch (.f64 #s(literal 2/3 binary64) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) (patch #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) #<representation binary64>) () ())

Outputs
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) (patch (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) (taylor 0 eps) (#s(alt (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) (patch (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) (patch (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) (patch (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())) ())
#s(alt (/ eps (cos x)) (taylor 0 eps) (#s(alt (/.f64 (sin.f64 eps) (cos.f64 x)) (patch (/.f64 (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x)))) (taylor 0 eps) (#s(alt (/.f64 (sin.f64 eps) (cos.f64 x)) (patch (/.f64 (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) (taylor 0 eps) (#s(alt (/.f64 (sin.f64 eps) (cos.f64 x)) (patch (/.f64 (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) (taylor 0 eps) (#s(alt (/.f64 (sin.f64 eps) (cos.f64 x)) (patch (/.f64 (sin.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/6 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x eps) x eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (pow x 2))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x eps) x eps) (patch (fma.f64 (.f64 x eps) x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (pow x 2))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x eps) x eps) (patch (fma.f64 (.f64 x eps) x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (pow x 2))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x eps) x eps) (patch (fma.f64 (.f64 x eps) x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (pow x 2))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x eps) x eps) (patch (fma.f64 (.f64 x eps) x eps) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor 0 eps) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor 0 eps) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor 0 eps) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor 0 eps) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(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)))) (taylor 0 eps) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) (patch (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) (patch (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) (patch (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) (patch (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps) #<representation binary64>) () ())) ())
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#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))) (patch #s(approx (/ 1 (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor -inf x) (#s(alt (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor -inf x) (#s(alt (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor -inf x) (#s(alt (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor -inf x) (#s(alt (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor -inf x) (#s(alt #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -2/45 (pow x 6)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) 2/45)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/45 (/ 1 (pow x 4))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (- (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 2/45 (/ 1 (pow x 4))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) (patch #s(approx (/ ( (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) (taylor -inf x) (#s(alt (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) (patch (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (patch (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (patch (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (patch (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (patch (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (* -2/45 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) (patch #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) (patch #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) (patch #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin eps)) (taylor -inf x) (#s(alt #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) (patch #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	eps	@	-inf	((* (/ (sin eps) (cos x)) (/ 1 (cos (+ x eps)))) (/ (sin eps) (cos x)) (sin eps) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (* x eps) x) eps) (* x eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (/ 1 (cos (+ x eps))) (* 2/3 eps) (+ (* -2/45 (* x x)) 1/3) (/ (cos x) (sin eps)))
6.0ms	eps	@	0	((* (/ (sin eps) (cos x)) (/ 1 (cos (+ x eps)))) (/ (sin eps) (cos x)) (sin eps) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (* x eps) x) eps) (* x eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (/ 1 (cos (+ x eps))) (* 2/3 eps) (+ (* -2/45 (* x x)) 1/3) (/ (cos x) (sin eps)))
4.0ms	eps	@	inf	((* (/ (sin eps) (cos x)) (/ 1 (cos (+ x eps)))) (/ (sin eps) (cos x)) (sin eps) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (* x eps) x) eps) (* x eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (/ 1 (cos (+ x eps))) (* 2/3 eps) (+ (* -2/45 (* x x)) 1/3) (/ (cos x) (sin eps)))
4.0ms	x	@	inf	((* (/ (sin eps) (cos x)) (/ 1 (cos (+ x eps)))) (/ (sin eps) (cos x)) (sin eps) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (* x eps) x) eps) (* x eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (/ 1 (cos (+ x eps))) (* 2/3 eps) (+ (* -2/45 (* x x)) 1/3) (/ (cos x) (sin eps)))
4.0ms	x	@	-inf	((* (/ (sin eps) (cos x)) (/ 1 (cos (+ x eps)))) (/ (sin eps) (cos x)) (sin eps) (cos x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (* x eps) x) eps) (* x eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* 2/3 eps) (* x x)) eps) (* x x)) eps) (+ (* (* 2/3 eps) (* x x)) eps) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ x eps)) (/ (cos x) (sin eps))) (cos (+ x eps)) (/ 1 (cos (+ x eps))) (* 2/3 eps) (+ (* -2/45 (* x x)) 1/3) (/ (cos x) (sin eps)))

simplify211.0ms (1.6%)

Memory

-12.2MiB live, 220.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 618×	`lower-fma.f64`
9 618×	`lower-fma.f32`
6 714×	`lower-*.f64`
6 714×	`lower-*.f32`
3 368×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	456	5750
1	1335	5584
2	4048	5372
0	8635	5136

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 497

Calls

Call 1

Inputs
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))
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))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (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 (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (pow (cos x) 2) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (pow (cos x) 2) eps)
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps)
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(/ 1 (cos x))
(+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(/ (cos x) eps)
(/ (+ (cos x) (* 1/6 (* (pow eps 2) (cos x)))) eps)
(/ (+ (cos x) (* (pow eps 2) (- (* -1 (* (pow eps 2) (+ (* -1/36 (cos x)) (* 1/120 (cos x))))) (* -1/6 (cos x))))) eps)
(/ (+ (cos x) (* (pow eps 2) (- (* (pow eps 2) (- (* -1 (* (pow eps 2) (+ (* -1/5040 (cos x)) (+ (* 1/720 (cos x)) (* 1/6 (+ (* -1/36 (cos x)) (* 1/120 (cos x)))))))) (+ (* -1/36 (cos x)) (* 1/120 (cos x))))) (* -1/6 (cos x))))) 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))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(sin eps)
(sin eps)
(sin eps)
(sin 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))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps x)
(* eps x)
(* eps x)
(* 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 x))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow x 2))))
(* eps (+ 1 (* 2/3 (pow 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))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (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))))
(/ (* (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 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 (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(sin eps)
(sin eps)
(sin eps)
(sin 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 (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* -1 (* eps (- (* -1 (pow x 2)) 1)))
(* -1 (* eps (- (* -1 (pow x 2)) 1)))
(* -1 (* eps (- (* -1 (pow x 2)) 1)))
(* -1 (* eps (- (* -1 (pow x 2)) 1)))
(* eps x)
(* eps x)
(* eps x)
(* 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)))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
(* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
(* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
(* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(/ (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)))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ (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)))))
(/ (* (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 (neg (* -1 eps))))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin eps))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin eps))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin eps))
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin eps))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(* 2/3 eps)
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (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)
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(/ (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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
(+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* eps (pow x 2)))
(+ eps (* eps (pow x 2)))
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(/ (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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
(+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
eps
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* 2/3 (* eps (pow x 2))))
(/ (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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
(+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(/ (sin eps) (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)))
(/ (cos eps) (sin eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin eps)))
(/ (cos eps) (sin eps))
(+ (* -1 x) (/ (cos eps) (sin eps)))
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps)))
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin eps)))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(/ 1 (cos eps))
(+ (/ 1 (cos eps)) (/ (* x (sin eps)) (pow (cos eps) 2)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1 (/ (* (sin eps) (- (* 1/2 (/ 1 (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (cos eps))) (+ (* -1/2 (/ (sin eps) (pow (cos eps) 2))) (* 1/6 (/ (sin eps) (pow (cos eps) 2))))))) (* 1/2 (/ 1 (cos eps)))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (* -1 (/ (sin eps) (pow (cos eps) 2))))) (/ 1 (cos eps)))
1/3
(+ 1/3 (* -2/45 (pow x 2)))
(+ 1/3 (* -2/45 (pow x 2)))
(+ 1/3 (* -2/45 (pow x 2)))
(/ 1 (sin eps))
(+ (* -1/2 (/ (pow x 2) (sin eps))) (/ 1 (sin eps)))
(+ (* (pow x 2) (- (* 1/24 (/ (pow x 2) (sin eps))) (* 1/2 (/ 1 (sin eps))))) (/ 1 (sin eps)))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/720 (/ (pow x 2) (sin eps))) (* 1/24 (/ 1 (sin eps))))) (* 1/2 (/ 1 (sin eps))))) (/ 1 (sin 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))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(cos x)
(cos x)
(cos x)
(cos 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 x))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* eps (pow x 2))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* eps x)
(* eps x)
(* eps x)
(* 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 x))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* 2/3 (* eps (pow x 4)))
(* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))
(* 2/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow 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))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(* -2/45 (pow x 6))
(* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/45 (/ 1 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 2/45 (/ 1 (pow x 4)))))
(/ (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))))
(/ (* (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 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 (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(* -2/45 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (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)))))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(cos x)
(cos x)
(cos x)
(cos 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 (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* eps (pow x 2))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* eps x)
(* eps x)
(* eps x)
(* 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 (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* 2/3 (* eps (pow x 4)))
(* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))
(* 2/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(/ (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 (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(* -2/45 (pow x 6))
(* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/45 (/ 1 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 2/45 (/ 1 (pow x 4)))))
(/ (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)))))
(/ (* (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)))) (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)))) (sin eps))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(* -2/45 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 2/45))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))
(/ (cos x) (sin eps))

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

rewrite212.0ms (1.6%)

Memory

13.6MiB live, 259.3MiB allocated

Rules

4 826×	`lower-fma.f32`
4 814×	`lower-fma.f64`
4 332×	`lower-*.f32`
4 322×	`lower-*.f64`
3 894×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	357
0	75	355
1	303	339
2	2069	339
0	8514	339

Stop Event

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

Counts

24 → 402

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(*.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))))
(*.f64 (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 (+.f64 x eps)))) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))) (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (neg.f64 (cos.f64 x))))
(*.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (neg.f64 (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))))
(*.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (/.f64 (cos.f64 x) (sin.f64 eps))))
(*.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 eps))) (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (cos.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 eps))) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (cos.f64 x)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 x)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 eps))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (cos.f64 (+.f64 x eps))) (/.f64 (neg.f64 (sin.f64 eps)) #s(literal 1 binary64)))
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (/.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) #s(literal 1 binary64)))
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(.f64 (/.f64 (sin.f64 eps) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sqrt.f64 (cos.f64 x))))
(*.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (cos.f64 x)) (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 eps))))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 (+.f64 x eps)))))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 eps))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sqrt.f64 (cos.f64 x))) (/.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) (/.f64 (sin.f64 eps) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 x))))
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))))
(*.f64 (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 x))) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (+.f64 x eps))))
(.f64 (/.f64 (sin.f64 eps) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 eps))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 (sin.f64 eps) #s(literal 1 binary64)))
(.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))))
(.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sin.f64 eps)) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (cos.f64 x) (sin.f64 eps))))
(.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x)))
(.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
(.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(pow.f64 (/.f64 (cos.f64 x) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 eps)))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal -1 binary64))) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (sin.f64 eps) (cos.f64 x)))) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 eps)))) (neg.f64 (.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps)))) (neg.f64 (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (.f64 (neg.f64 (sin.f64 eps)) #s(literal -1 binary64))) (neg.f64 (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps))))))
(/.f64 (neg.f64 (.f64 (neg.f64 (sin.f64 eps)) #s(literal 1 binary64))) (neg.f64 (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (.f64 (sin.f64 eps) #s(literal -1 binary64))) (neg.f64 (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) (neg.f64 (/.f64 (cos.f64 x) (sin.f64 eps))))
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 eps))) (neg.f64 (cos.f64 x)))
(/.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal -1 binary64)) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (neg.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (/.f64 (sin.f64 eps) (cos.f64 x))) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 eps))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 eps))) (.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 eps))) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (.f64 (neg.f64 (sin.f64 eps)) #s(literal -1 binary64)) (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (.f64 (neg.f64 (sin.f64 eps)) #s(literal 1 binary64)) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (.f64 (sin.f64 eps) #s(literal -1 binary64)) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 x) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (cos.f64 x) (sin.f64 eps))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (cos.f64 x) (sin.f64 eps)))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (cos.f64 x) (sin.f64 eps)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) (neg.f64 (cos.f64 (+.f64 x eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))) (/.f64 (sin.f64 eps) (.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(*.f64 (/.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (cos.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (cos.f64 x))) (/.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x))))
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(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (cos.f64 (-.f64 x eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(/.f64 (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))))
(/.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
(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)))))
(fma.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 x eps))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (cos.f64 (-.f64 x eps))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))))))
(-.f64 (/.f64 (/.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 1 binary64)) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (.f64 (sin.f64 x) (sin.f64 eps))))
(exp.f64 (neg.f64 (*.f64 (log.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64))))
(*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
(pow.f64 (exp.f64 (log.f64 (cos.f64 (+.f64 x eps)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))) #s(literal -1 binary64))
(pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(neg.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))))
(exp.f64 (*.f64 (log.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)))
(*.f64 #s(literal 2/3 binary64) eps)
(*.f64 eps #s(literal 2/3 binary64))
(.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
(.f64 (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 (*.f64 x x) #s(literal -2/135 binary64))))))
(pow.f64 (/.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/9 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -2/135 binary64)))) (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/9 binary64) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (/.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (fma.f64 (/.f64 #s(literal 1/9 binary64) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (.f64 (/.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 #s(literal -2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/45 binary64) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/9 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -2/135 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (fma.f64 #s(literal -2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/45 binary64) (.f64 x x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/9 binary64))) (neg.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64))) (neg.f64 (+.f64 #s(literal 1/9 binary64) (-.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -2/135 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64))) (neg.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -2/135 binary64))))))
(/.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/9 binary64)) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64)) (+.f64 #s(literal 1/9 binary64) (-.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -2/135 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64)) (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -2/135 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/9 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -2/135 binary64)))) (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/9 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -2/135 binary64)))) (fma.f64 (.f64 #s(literal -8/91125 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1/27 binary64))))
(fma.f64 (*.f64 #s(literal -2/45 binary64) x) x #s(literal 1/3 binary64))
(fma.f64 #s(literal -2/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64))
(fma.f64 x (*.f64 #s(literal -2/45 binary64) x) #s(literal 1/3 binary64))
(-.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/45 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/45 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 4/2025 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
(+.f64 (.f64 #s(literal -2/45 binary64) (.f64 x x)) #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/45 binary64) (.f64 x x)))
#s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps))

eval212.0ms (1.6%)

Memory: 2.8MiB live, 193.8MiB allocated
Compiler: Compiled 21 524 to 1 669 computations (92.2% saved)

prune159.0ms (1.2%)

Memory

3.6MiB live, 202.2MiB allocated

Pruning

28 alts after pruning (22 fresh and 6 done)

	Pruned	Kept	Total
New	976	9	985
Fresh	5	13	18
Picked	1	4	5
Done	0	2	2
Total	982	28	1 010

Accuracy

100.0%

Counts

1 010 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (*.f64 (cos.f64 x) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) eps)))
✓	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))))
	98.5%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)))))
	98.3%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.7%	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
	99.7%	(.f64 (/.f64 #s(approx (sin eps) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 eps))
	34.9%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 eps eps))))
	55.2%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 eps))))
	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
✓	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	98.7%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
	98.1%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(literal 1 binary64)))))
	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps 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))))) eps))
	98.7%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
✓	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
✓	98.5%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps)))
	6.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x eps) x) eps) (.f64 (.f64 x eps) x))))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps))))

Compiler

Compiled 1 483 to 488 computations (67.1% saved)

regimes70.0ms (0.5%)

Memory

-14.8MiB live, 70.3MiB allocated

Counts

58 → 1

Calls

Call 1

Inputs
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x eps) x) eps) (.f64 (.f64 x eps) x))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps))) eps eps))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps 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))))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 eps))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 eps eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))))
(.f64 (/.f64 #s(approx (sin eps) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 eps))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (sin.f64 eps)))))
(*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (*.f64 (cos.f64 x) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
(/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 #s(literal 0 binary64) eps))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (.f64 (.f64 (+.f64 (+.f64 x eps) x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x eps) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (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 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

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

Calls

3 calls:

29.0ms	x
22.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes50.0ms (0.4%)

Memory

-4.8MiB live, 33.3MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x eps) x) eps) (.f64 (.f64 x eps) x))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps))) eps eps))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (fma.f64 (.f64 (.f64 eps eps) eps) #s(literal 1/3 binary64) eps))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps 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))))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 eps))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)))))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 eps eps))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (*.f64 (cos.f64 (+.f64 x eps)) #s(approx (/ (cos x) (sin eps)) (/.f64 (cos.f64 x) eps)))))
(.f64 (/.f64 #s(approx (sin eps) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 eps))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))

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

Calls

3 calls:

26.0ms	x
11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes37.0ms (0.3%)

Memory

6.1MiB live, 42.1MiB allocated

Counts

37 → 1

Calls

Call 1

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

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

Calls

3 calls:

15.0ms	x
10.0ms	eps
10.0ms	(-.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)

regimes34.0ms (0.3%)

Memory

2.0MiB live, 46.6MiB allocated

Counts

32 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	eps
9.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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)

regimes29.0ms (0.2%)

Memory

6.8MiB live, 43.5MiB allocated

Counts

30 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	eps
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes28.0ms (0.2%)

Memory

-3.9MiB live, 34.3MiB allocated

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

10.0ms	eps
8.0ms	x
8.0ms	(-.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)

regimes33.0ms (0.2%)

Memory

-5.0MiB live, 33.1MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

21.0ms	eps
6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes21.0ms (0.2%)

Memory

-13.7MiB live, 31.4MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

9.0ms	x
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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)

regimes14.0ms (0.1%)

Memory

26.9MiB live, 26.9MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

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)

regimes14.0ms (0.1%)

Memory

-14.4MiB live, 22.5MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	eps
3.0ms	x
3.0ms	(-.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)

regimes10.0ms (0.1%)

Memory

22.2MiB live, 22.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

regimes9.0ms (0.1%)

Memory

-20.4MiB live, 15.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	eps
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)

regimes4.0ms (0%)

Memory

12.5MiB live, 12.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
6.3%	1	`x`
6.3%	1	`eps`
6.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-17.6MiB live, 20.3MiB allocated

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	457
1	147	457

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (11.3%)

Memory

11.9MiB live, 1 055.9MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
13 218×	`lower-fma.f64`
13 218×	`lower-fma.f32`
11 350×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	580	10406
1	1818	10139
2	6122	9942
0	8323	9547
0	75	723
0	106	719
1	506	548
2	4737	536
0	8169	506
0	456	5750
1	1335	5584
2	4048	5372
0	8635	5136
0	61	487
0	113	472
1	505	369
2	4635	369
0	8175	353
0	709	11463
1	2285	11197
2	7608	11093
0	8838	10702
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	157	1351
1	464	1285
2	1534	1274
3	5964	1242
0	8538	1195

Stop Event

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

Compiler

Compiled 834 to 419 computations (49.8% saved)

preprocess140.0ms (1%)

Memory: -0.9MiB live, 189.6MiB allocated
Compiler: Compiled 444 to 162 computations (63.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze41.0ms (0.3%)

sample6.6s (48.9%)

explain111.0ms (0.8%)

preprocess27.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize36.0ms (0.3%)

series38.0ms (0.3%)

simplify200.0ms (1.5%)

rewrite255.0ms (1.9%)

eval55.0ms (0.4%)

prune186.0ms (1.4%)

simplify163.0ms (1.2%)

localize290.0ms (2.2%)

series99.0ms (0.7%)

simplify216.0ms (1.6%)

rewrite231.0ms (1.7%)

eval250.0ms (1.9%)

prune172.0ms (1.3%)

simplify156.0ms (1.2%)

localize211.0ms (1.6%)

series65.0ms (0.5%)

simplify243.0ms (1.8%)

rewrite210.0ms (1.6%)

eval213.0ms (1.6%)

prune175.0ms (1.3%)

simplify176.0ms (1.3%)

localize131.0ms (1%)

series68.0ms (0.5%)

simplify211.0ms (1.6%)

rewrite212.0ms (1.6%)

eval212.0ms (1.6%)

prune159.0ms (1.2%)

regimes70.0ms (0.5%)

regimes50.0ms (0.4%)

regimes37.0ms (0.3%)

regimes34.0ms (0.3%)

regimes29.0ms (0.2%)

regimes28.0ms (0.2%)

regimes33.0ms (0.2%)

regimes21.0ms (0.2%)

regimes14.0ms (0.1%)

regimes14.0ms (0.1%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes4.0ms (0%)

simplify10.0ms (0.1%)

soundness1.5s (11.3%)

preprocess140.0ms (1%)

end0.0ms (0%)

Profiling

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

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