Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze48.0ms (0.3%)

Memory

5.5MiB live, 51.7MiB 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)

sample6.3s (42.9%)

Memory

-172.9MiB live, 7 256.1MiB allocated

Samples

3.4s	26 447×	0	invalid
679.0ms	5 425×	0	valid
461.0ms	2 831×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

const: 729.0ms (21.4% of total)

ival-tan: 677.0ms (19.8% of total)

ival-mult: 434.0ms (12.7% of total)

ival-<=: 422.0ms (12.4% of total)

ival-add: 257.0ms (7.5% of total)

ival-fabs: 251.0ms (7.4% of total)

ival-sub: 245.0ms (7.2% of total)

ival-<: 156.0ms (4.6% of total)

ival-and: 105.0ms (3.1% of total)

adjust: 77.0ms (2.3% of total)

exact: 44.0ms (1.3% of total)

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

Bogosity

explain119.0ms (0.8%)

Memory

-33.8MiB live, 165.5MiB 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

25.0ms	6×	3	valid
21.0ms	162×	1	valid
16.0ms	342×	0	valid
3.0ms	2×	2	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-tan: 35.0ms (77.3% of total)

adjust: 4.0ms (8.8% of total)

ival-add: 3.0ms (6.6% of total)

ival-sub: 3.0ms (6.6% of total)

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

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

preprocess23.0ms (0.2%)

Memory

37.1MiB live, 37.1MiB 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))

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB 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)

simplify15.0ms (0.1%)

Memory

-24.4MiB live, 12.3MiB 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))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)

localize43.0ms (0.3%)

Memory

23.6MiB live, 63.2MiB 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

19.0ms	3×	3	valid
8.0ms	171×	0	valid
8.0ms	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: 29.0ms

ival-tan: 23.0ms (80.3% of total)

adjust: 2.0ms (7% of total)

ival-add: 2.0ms (7% of total)

ival-sub: 1.0ms (3.5% of total)

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

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

series13.0ms (0.1%)

Memory

-17.3MiB live, 21.2MiB 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 (/ (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 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 (* -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 (* 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 (+ 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 (- 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 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 (/ (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 (/ (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 (/ (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 (/ (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 (/ (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 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 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 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 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 (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 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 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 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 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

21 calls:

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

simplify268.0ms (1.8%)

Memory

17.1MiB live, 297.5MiB 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	5949	1242
0	8534	1195

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite264.0ms (1.8%)

Memory

-12.6MiB live, 254.6MiB 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
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)))
(+.f64 (tan.f64 (+.f64 x eps)) (neg.f64 (tan.f64 x)))
(+.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (/.f64 (.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))
(-.f64 (+.f64 (tan.f64 (+.f64 x eps)) #s(literal 0 binary64)) (tan.f64 x))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (tan.f64 x) #s(literal -1 binary64) (tan.f64 (+.f64 x eps)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
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(.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x))))))
(.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(.f64 (neg.f64 (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
(.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps (-.f64 eps x)) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))
(tan.f64 x)
(neg.f64 (neg.f64 (tan.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

eval40.0ms (0.3%)

Memory: 22.1MiB live, 68.3MiB allocated
Compiler: Compiled 8 701 to 985 computations (88.7% saved)

prune58.0ms (0.4%)

Memory

-2.0MiB live, 111.8MiB 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) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
	62.5%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
	61.5%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
	62.5%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	62.5%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x))))
	62.6%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	62.5%	(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
▶	62.6%	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
▶	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)))
▶	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (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 (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 751 to 380 computations (49.4% saved)

simplify303.0ms (2.1%)

Memory

15.2MiB live, 301.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (tan.f64 x) (tan.f64 eps))
cost-diff	0	(/.f64 (+.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))))
cost-diff	0	(.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
cost-diff	0	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
cost-diff	0	(/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x)))
cost-diff	384	(-.f64 (+.f64 x eps) x)
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) 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) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 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) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (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 (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
cost-diff	192	(+.f64 (-.f64 (/.f64 (+.f64 (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 (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64))
cost-diff	5824	(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (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 (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
cost-diff	26816	(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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))

Rules

14 762×	`lower-fma.f32`
14 748×	`lower-fma.f64`
4 348×	`lower-*.f32`
4 338×	`lower-*.f64`
2 728×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	774
0	111	770
1	199	690
2	474	679
3	1275	673
4	4134	673
5	7633	673
0	8290	663

Stop Event

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

Calls

Call 1

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

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

localize310.0ms (2.1%)

Memory

10.0MiB live, 477.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (tan.f64 x) (tan.f64 eps))
accuracy	0.01953125	(+.f64 (tan.f64 x) (tan.f64 eps))
accuracy	0.10775375976844201	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))
accuracy	23.918482892439503	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x))))
accuracy	23.96972852167959	(-.f64 (+.f64 x eps) x)
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(/.f64 (sin.f64 x) (cos.f64 x))
accuracy	0.07219329735525831	(tan.f64 (+.f64 x eps))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy	0.07219329735525831	(tan.f64 (+.f64 x eps))
accuracy	0.296875	(*.f64 x #s(literal 1/3 binary64))
accuracy	0.9033645080441755	#s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) x)))
accuracy	0.033535009768442016	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.109375	(fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (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 (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (-.f64 (/.f64 (+.f64 (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 (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
accuracy	0.9889450195368841	(+.f64 (-.f64 (/.f64 (+.f64 (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 (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal -1/6 binary64))

Samples

95.0ms	162×	0	valid
85.0ms	88×	1	valid
23.0ms	4×	3	valid
6.0ms	2×	2	valid

Compiler

Compiled 704 to 62 computations (91.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 175.0ms

ival-mult: 28.0ms (16% of total)

ival-tan: 26.0ms (14.9% of total)

ival-div: 22.0ms (12.6% of total)

ival-add: 20.0ms (11.4% of total)

const: 14.0ms (8% of total)

adjust: 14.0ms (8% of total)

ival-sin: 14.0ms (8% of total)

ival-pow: 13.0ms (7.4% of total)

ival-pow2: 10.0ms (5.7% of total)

ival-sub: 8.0ms (4.6% of total)

ival-cos: 5.0ms (2.9% of total)

exact: 1.0ms (0.6% of total)

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

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

series149.0ms (1%)

Memory

-36.5MiB live, 212.2MiB allocated

Counts

25 → 516

Calls

Call 1

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

Outputs
#s(alt -1/2 (taylor 0 x) (#s(alt (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/3 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) (taylor 0 x) (#s(alt (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (patch (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))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
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#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 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (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)))) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (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)))) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #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 eps) (#s(alt (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* x (sin eps)) (cos eps)) (taylor 0 x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) (taylor 0 x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) (taylor 0 x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) (taylor 0 x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* eps (sin x)) (cos x)) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())

Calls

129 calls:

Time	Variable		Point	Expression
24.0ms	x	@	inf	(+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
10.0ms	x	@	-inf	(+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))
8.0ms	eps	@	0	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x))
6.0ms	eps	@	inf	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x))
5.0ms	eps	@	0	(/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x))))

simplify345.0ms (2.4%)

Memory

34.5MiB live, 420.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 202×	`lower-fma.f64`
13 202×	`lower-fma.f32`
7 778×	`lower-*.f64`
7 778×	`lower-*.f32`
4 264×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	707	11420
1	2277	11159
2	7594	11055
0	8825	10673

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 484

Calls

Call 1

Inputs
-1/2
(- (* -1/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(- (+ (* -1/2 (/ (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)
(- (+ (* -1/2 (/ (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)
(* 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 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 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))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (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)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* 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)))))
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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))))))
(* (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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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)))
(+ (* 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 3)
(* (pow x 3) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 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)))
(/ (* (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)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (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))))
(/ (* (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)))
(/ (* (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)))
(/ (* x (sin eps)) (cos eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(/ (* (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)))
(/ (* (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)))
(/ (* 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))))
(/ (* (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)))
(/ (* (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
-1/2
#s(literal -1/2 binary64)
(- (* -1/3 (pow x 2)) 1/2)
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -2/9 binary64) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -17/135 binary64)) #s(literal -2/9 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(* 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 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (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 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (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 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 eps (.f64 (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (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 eps eps)))
(* (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 eps (.f64 eps eps)) (+.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) (+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) 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))))
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(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps))) (neg.f64 (sin.f64 x))) (cos.f64 x))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(/.f64 (.f64 x (.f64 x (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 17/45 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 17/45 binary64) (/.f64 (.f64 (.f64 #s(literal 62/315 binary64) (.f64 x x)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 eps eps))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 #s(literal 2/3 binary64) (.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) (+ (* (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))))
(.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 2/3 binary64) (.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 #s(literal 17/45 binary64) (.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) (+ (* (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))))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 17/45 binary64) (/.f64 (.f64 (.f64 #s(literal 62/315 binary64) (.f64 eps eps)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* x (sin eps)) (cos eps))
(/.f64 (*.f64 x (sin.f64 eps)) (cos.f64 eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(.f64 x (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x (*.f64 x #s(literal 1/3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 2/15 binary64) (sin.f64 eps)) (cos.f64 eps)) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps))) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 2/15 binary64) (/.f64 (.f64 #s(literal 17/315 binary64) (.f64 x (.f64 x (sin.f64 eps)))) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps))) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* eps (sin x)) (cos x))
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(.f64 eps (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (.f64 (.f64 (*.f64 eps eps) #s(literal 2/15 binary64)) (sin.f64 x)) (cos.f64 x))) (/.f64 (sin.f64 x) (cos.f64 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))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 2/15 binary64) (.f64 (.f64 #s(literal 17/315 binary64) (.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))

rewrite509.0ms (3.5%)

Memory

-29.8MiB live, 299.9MiB allocated

Rules

5 070×	`lower-fma.f32`
5 056×	`lower-fma.f64`
5 040×	`lower-*.f32`
5 030×	`lower-*.f64`
2 338×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	484
0	111	469
1	505	358
2	4692	358
0	8228	344

Stop Event

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

Counts

25 → 674

Calls

Call 1

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

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

eval590.0ms (4%)

Memory: 37.7MiB live, 350.6MiB allocated
Compiler: Compiled 62 351 to 4 017 computations (93.6% saved)

prune167.0ms (1.1%)

Memory

-17.6MiB live, 307.7MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	1 458	12	1 470
Fresh	11	0	11
Picked	5	0	5
Done	0	1	1
Total	1 474	13	1 487

Accuracy

100.0%

Counts

1 487 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x))) (/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (sin.f64 x) (.f64 (cos.f64 x) eps))) eps)))
	99.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x))) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.9%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
▶	99.2%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
▶	99.3%	#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	99.7%	#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x)) (fma.f64 eps (fma.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.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))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps #s(approx (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6) #s(literal 1/3 binary64)) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))

Compiler

Compiled 577 to 288 computations (50.1% saved)

simplify350.0ms (2.4%)

Memory

-29.5MiB live, 422.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

16 882×	`lower-fma.f32`
16 870×	`lower-fma.f64`
4 144×	`lower-*.f32`
4 138×	`lower-*.f64`
3 182×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	783
0	112	783
1	216	699
2	511	691
3	1356	687
4	3882	687
5	7000	687
0	8156	664

Stop Event

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

Calls

Call 1

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

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

localize257.0ms (1.8%)

Memory

34.8MiB live, 348.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy	0.01171875	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.015625	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.4745618093409555	#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (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))
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 x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.13671875	(fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
accuracy	0.17578125	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	1.2060271157130906	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
accuracy	0.00390625	(fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps)
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
accuracy	0.17578125	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
accuracy	31.424916395330225	#s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
accuracy	0	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
accuracy	0.01171875	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))

Samples

100.0ms	171×	0	valid
84.0ms	81×	1	valid
4.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 532 to 70 computations (86.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-add: 33.0ms (20.1% of total)

ival-mult: 30.0ms (18.3% of total)

ival-div: 23.0ms (14% of total)

ival-pow: 18.0ms (11% of total)

adjust: 13.0ms (7.9% of total)

const: 12.0ms (7.3% of total)

ival-pow2: 11.0ms (6.7% of total)

ival-sub: 7.0ms (4.3% of total)

ival-tan: 6.0ms (3.7% of total)

ival-cos: 5.0ms (3.1% of total)

ival-sin: 5.0ms (3.1% of total)

exact: 1.0ms (0.6% of total)

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

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

series51.0ms (0.3%)

Memory

-4.1MiB live, 65.4MiB allocated

Counts

21 → 432

Calls

Call 1

Inputs
#s(alt #s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) (patch #s(approx (/ 1 (/ ( (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps) (patch (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps) #<representation binary64>) () ())
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Outputs
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#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (patch (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) (taylor 0 x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) (taylor 0 x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) (taylor 0 x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 2) (taylor inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 2) (taylor inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 2) (taylor inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 2) (taylor inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 2) (taylor -inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (cos eps) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* -1 (* x (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
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#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps 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>) () ())) ())
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#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 x) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
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#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (+ eps x)) (taylor inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- x (* -1 eps))) (taylor -inf eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())

Calls

108 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps)))
1.0ms	eps	@	0	(+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps)
1.0ms	x	@	inf	(+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps)
1.0ms	x	@	-inf	(+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps)
1.0ms	eps	@	inf	(/ eps (pow (cos x) 2))

simplify268.0ms (1.8%)

Memory

14.0MiB live, 336.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 866×	`lower-fma.f64`
10 866×	`lower-fma.f32`
6 462×	`lower-*.f64`
6 462×	`lower-*.f32`
3 730×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	585	10800
1	1893	10543
2	6392	10357
0	8038	9931

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 429

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin 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 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (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 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 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))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (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)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* 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)))))
(/ (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 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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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)))
(+ (* 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)))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (/ eps x)))))
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2))))
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (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 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 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))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (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)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* 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)))))
(/ (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 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 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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)))
(+ (* 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) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
eps
(+ eps (* eps (pow x 2)))
(+ 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 (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps)))
(- (/ (* (+ 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))))) (/ (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)))
(* 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)))))
(- (/ (* (+ 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))))) (/ (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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))

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

rewrite373.0ms (2.6%)

Memory

11.8MiB live, 284.5MiB allocated

Rules

6 016×	`lower-fma.f32`
6 004×	`lower-fma.f64`
5 410×	`lower-*.f32`
5 404×	`lower-*.f64`
2 470×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	729
0	112	729
1	559	540
2	5107	540
0	8489	509

Stop Event

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

Counts

21 → 223

Calls

Call 1

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

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

eval86.0ms (0.6%)

Memory: -32.8MiB live, 127.4MiB allocated
Compiler: Compiled 18 955 to 1 111 computations (94.1% saved)

prune166.0ms (1.1%)

Memory

18.7MiB live, 147.8MiB allocated

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	714	18	732
Fresh	2	5	7
Picked	3	2	5
Done	0	1	1
Total	719	26	745

Accuracy

100.0%

Counts

745 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x))) (/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (sin.f64 x) (.f64 (cos.f64 x) eps))) eps)))
	99.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x))) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	99.9%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
	99.7%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (.f64 eps (sin.f64 x)))))))
▶	98.6%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))))
	99.7%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
	99.3%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) 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 x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
	98.7%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
	98.1%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
▶	99.9%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))))
	99.3%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) 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))
	99.9%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (sin.f64 eps)))
▶	98.6%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps)))
▶	98.5%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
	98.7%	#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))
	98.7%	#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.f64 (/.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))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (fma.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) x) (.f64 x x)))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (+.f64 (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) (/.f64 x eps))))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (*.f64 x (+.f64 eps x)))) eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))

Compiler

Compiled 932 to 480 computations (48.5% saved)

simplify232.0ms (1.6%)

Memory

17.9MiB live, 237.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
cost-diff	0	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))))
cost-diff	0	(.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))
cost-diff	0	#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps)))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))
cost-diff	320	(fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps)
cost-diff	0	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps))
cost-diff	0	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 eps (*.f64 x x) eps)
cost-diff	0	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps))
cost-diff	0	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (cos.f64 x))
cost-diff	0	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))))
cost-diff	704	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))

Rules

12 962×	`lower-fma.f32`
12 946×	`lower-fma.f64`
3 786×	`lower-*.f32`
3 770×	`lower-*.f64`
2 984×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	587
0	112	577
1	233	545
2	578	529
3	1658	521
4	4642	521
0	8056	513

Stop Event

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

Calls

Call 1

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

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

localize292.0ms (2%)

Memory

-23.6MiB live, 388.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
accuracy	0.015625	(.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0.9155432572496691	#s(approx (cos x) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	0.05859375	(.f64 eps (.f64 eps eps))
accuracy	0.140625	(.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))))
accuracy	0.9227018729721077	#s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps)))
accuracy	0.00390625	(fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps)
accuracy	0.23046875	(.f64 (.f64 x x) #s(literal 2/3 binary64))
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps)))
accuracy	0.8186173525058796	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps))
accuracy	0	(fma.f64 eps (*.f64 x x) eps)
accuracy	0	(*.f64 x x)
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
accuracy	0.9227288180468125	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps))
accuracy	0	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))))
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

124.0ms	171×	0	valid
96.0ms	81×	1	valid
4.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 370 to 76 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 171.0ms

ival-mult: 56.0ms (32.8% of total)

ival-add: 22.0ms (12.9% of total)

ival-div: 20.0ms (11.7% of total)

ival-pow: 18.0ms (10.5% of total)

const: 15.0ms (8.8% of total)

adjust: 14.0ms (8.2% of total)

ival-pow2: 6.0ms (3.5% of total)

ival-cos: 5.0ms (2.9% of total)

ival-sin: 5.0ms (2.9% of total)

ival-sub: 4.0ms (2.3% of total)

ival-tan: 4.0ms (2.3% of total)

exact: 1.0ms (0.6% of total)

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

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

series46.0ms (0.3%)

Memory

7.6MiB live, 80.7MiB allocated

Counts

23 → 492

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 #s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))))) (patch #s(approx (/ 1 (/ ( (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (*.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 #s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (.f64 x x) eps))) (patch #s(approx (/ 1 (/ ( (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (.f64 x x) eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 x x) eps) (patch (fma.f64 eps (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (.f64 x x) #s(literal 2/3 binary64)) eps) eps))) (patch #s(approx (/ 1 (/ ( (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps))) #<representation binary64>) () ())
#s(alt #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (.f64 x x) #s(literal 2/3 binary64)) eps) eps)) (patch #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (.f64 x x) #s(literal 2/3 binary64)) eps) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (.f64 x x) #s(literal 2/3 binary64)) eps) eps) (patch (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (.f64 x x) #s(literal 2/3 binary64)) eps) eps) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps)) (patch (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps)))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))) (patch #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)) eps))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) (patch (.f64 eps (fma.f64 x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))) (patch #s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))) (patch (/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))) (patch (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.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 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())
#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<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 (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf 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 (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf 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 (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf 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 (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf 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 (/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf 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 (/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf 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 (/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf 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 (/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) (taylor -inf 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>) () ())) ())
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#s(alt (+ (* 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))) (taylor 0 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 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 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 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 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 (/ 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 x)) (taylor 0 eps) (#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 x)) (/ (* eps (sin x)) (pow (cos x) 2))) (taylor 0 eps) (#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 (+ (* 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))) (taylor 0 eps) (#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 (+ (* 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))) (taylor 0 eps) (#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 x))) (taylor inf eps) (#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 x))) (taylor inf eps) (#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 x))) (taylor inf eps) (#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 x))) (taylor inf eps) (#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 (- x (* -1 eps)))) (taylor -inf eps) (#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 (- x (* -1 eps)))) (taylor -inf eps) (#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 (- x (* -1 eps)))) (taylor -inf eps) (#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 (- x (* -1 eps)))) (taylor -inf eps) (#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 (* 2/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 2/3 binary64)) (patch (.f64 (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor 0 eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 3) (taylor -inf eps) (#s(alt (.f64 eps (.f64 eps eps)) (patch (.f64 eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (patch #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

123 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(+ (* x (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (+ (* 1/3 (* eps (* eps eps))) eps))
1.0ms	eps	@	0	(+ (* eps (* x x)) eps)
1.0ms	eps	@	0	(+ (* (* x x) (+ (* eps (* (* x x) 2/3)) eps)) eps)
1.0ms	x	@	0	(/ 1 (cos (+ x eps)))
1.0ms	eps	@	0	(/ 1 (cos (+ x eps)))

simplify340.0ms (2.3%)

Memory

-10.9MiB live, 263.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 882×	`lower-fma.f64`
9 882×	`lower-fma.f32`
6 812×	`lower-*.f64`
6 812×	`lower-*.f32`
3 694×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	609	7721
1	1949	7444
2	6675	7349
0	8019	7026

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 487

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))))
(/ (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 (- 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 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ 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))))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(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)))))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (cos x))
(/ (sin eps) (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))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(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) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
eps
(+ eps (* eps (pow x 2)))
(+ 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 (pow (cos x) 2))
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(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow 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
(+ eps (* eps (pow x 2)))
(+ eps (* eps (pow x 2)))
(+ eps (* eps (pow 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 (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))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(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)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
eps
(+ eps (* eps (pow x 2)))
(+ 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 (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
(/ eps (pow (cos x) 2))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow 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 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)))))
(* 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 (* (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))))))
(* -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)))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ eps (pow x 2)) (/ (pow eps 2) x)))))
(* (pow x 2) (+ (* 1/3 (/ (pow eps 3) (pow x 2))) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ eps (pow x 2)) (/ (pow eps 2) x)))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))
(* eps (+ 1 (pow x 2)))
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(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))
(* -1 (* (pow eps 3) (- (* -4/3 (pow x 2)) 1/3)))
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3)))
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3)))
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (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 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 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))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (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)))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+ (* 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 x)
(* eps (+ eps x))
(* eps (+ x (* eps (+ 1 (* 4/3 (* eps x))))))
(* eps (+ x (* eps (+ 1 (* 4/3 (* eps x))))))
(* 4/3 (* (pow eps 3) x))
(* (pow eps 3) (+ (* 4/3 x) (/ 1 eps)))
(* (pow eps 3) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))
(* (pow eps 3) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))
(* 4/3 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (- (* -4/3 x) (/ 1 eps))))
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps)))))
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps)))))
(pow eps 2)
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))
(* eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)))
(* eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) 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)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin 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 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(/ 1 (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 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 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)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)

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

rewrite297.0ms (2%)

Memory

-4.1MiB live, 325.6MiB allocated

Rules

5 822×	`lower-fma.f32`
5 806×	`lower-fma.f64`
5 430×	`lower-*.f32`
5 414×	`lower-*.f64`
2 348×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	510
0	112	498
1	568	410
2	5076	410
0	8317	398

Stop Event

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

Counts

23 → 239

Calls

Call 1

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

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

eval97.0ms (0.7%)

Memory: 27.0MiB live, 182.7MiB allocated
Compiler: Compiled 17 983 to 1 135 computations (93.7% saved)

prune157.0ms (1.1%)

Memory

-25.7MiB live, 216.4MiB allocated

Pruning

27 alts after pruning (22 fresh and 5 done)

	Pruned	Kept	Total
New	811	7	818
Fresh	3	15	18
Picked	3	2	5
Done	0	3	3
Total	817	27	844

Accuracy

100.0%

Counts

844 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x))) (/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (sin.f64 x) (.f64 (cos.f64 x) eps))) eps)))
	99.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x))) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	99.9%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
	99.7%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (.f64 eps (sin.f64 x)))))))
	98.6%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)) (.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps)))))
	99.3%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) 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 x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/45 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
	98.7%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
	98.1%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
	99.7%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (.f64 eps (sin.f64 x)))))))
	99.7%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (.f64 (/.f64 #s(approx (sin eps) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))))
	99.3%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) 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))
	99.9%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (sin.f64 eps)))
	99.6%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) (*.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))))
✓	98.6%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 eps (.f64 (*.f64 x x) #s(literal 2/3 binary64)) eps) eps)))
✓	98.5%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
	6.3%	#s(approx (/ 1 (/ (* (cos x) (cos (+ x eps))) (sin (- (+ x eps) x)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* eps (* x x)) eps) (.f64 eps (.f64 x x)))))
	98.7%	#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))
	98.7%	#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 x eps (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (.f64 (.f64 eps eps) (+.f64 (fma.f64 x (*.f64 x #s(literal 4/3 binary64)) #s(literal 1/3 binary64)) (/.f64 x eps))))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* x (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (* 1/3 (* eps eps))) (*.f64 x (+.f64 eps x)))) eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) (fma.f64 x #s(approx (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps)) (.f64 eps (+.f64 eps x))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)) eps))))
	5.8%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* eps (+ (* eps (+ (* eps (+ (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))) -1/6)) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps) #s(approx (+ (* x (* eps (+ (* x (+ (* (* eps eps) 4/3) 1)) eps))) (+ (* 1/3 (* eps (* eps eps))) eps)) (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/3 binary64) (fma.f64 x (.f64 x #s(literal 4/3 binary64)) (/.f64 x eps))))))))

Compiler

Compiled 1 436 to 450 computations (68.7% saved)

regimes44.0ms (0.3%)

Memory

33.0MiB live, 71.6MiB allocated

Counts

54 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes76.0ms (0.5%)

Memory

2.7MiB live, 41.0MiB allocated

Counts

37 → 1

Calls

Call 1

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

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

Calls

3 calls:

55.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps
9.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes56.0ms (0.4%)

Memory

-19.5MiB live, 66.9MiB allocated

Counts

35 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes32.0ms (0.2%)

Memory

-16.4MiB live, 56.5MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.2%)

Memory

26.7MiB live, 26.7MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes28.0ms (0.2%)

Memory

-14.7MiB live, 24.2MiB allocated

Counts

29 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	eps
8.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.2%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

27 → 1

Calls

Call 1

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

Outputs

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

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.2%)

Memory

-26.3MiB live, 22.5MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms	x
6.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

-10.7MiB live, 27.2MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

#s(approx (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ (* (tan x) (tan eps)) 1)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64)) #s(literal 2/3 binary64)) #s(literal 1 binary64)))) eps eps))

Calls

3 calls:

7.0ms	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)

regimes16.0ms (0.1%)

Memory

26.5MiB live, 26.5MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

5.0ms	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)

regimes13.0ms (0.1%)

Memory

-19.0MiB live, 19.4MiB allocated

Counts

11 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

regimes10.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-19.9MiB live, 17.3MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

6.0ms	eps
3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	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)

regimes6.0ms (0%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

2.0ms	(-.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

9.9MiB live, 9.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

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)

simplify16.0ms (0.1%)

Memory

-23.1MiB live, 16.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	617
1	167	617

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (10.1%)

Memory

48.7MiB live, 1 031.9MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
13 202×	`lower-fma.f64`
13 202×	`lower-fma.f32`
10 866×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	609	7721
1	1949	7444
2	6675	7349
0	8019	7026
0	157	1351
1	464	1285
2	1534	1274
3	5949	1242
0	8534	1195
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	707	11420
1	2277	11159
2	7594	11055
0	8825	10673
0	79	729
0	112	729
1	559	540
2	5107	540
0	8489	509
0	585	10800
1	1893	10543
2	6392	10357
0	8038	9931

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

Compiler

Compiled 776 to 408 computations (47.4% saved)

preprocess186.0ms (1.3%)

Memory: 7.0MiB live, 196.3MiB allocated
Compiler: Compiled 532 to 176 computations (66.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze48.0ms (0.3%)

sample6.3s (42.9%)

explain119.0ms (0.8%)

preprocess23.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.1%)

localize43.0ms (0.3%)

series13.0ms (0.1%)

simplify268.0ms (1.8%)

rewrite264.0ms (1.8%)

eval40.0ms (0.3%)

prune58.0ms (0.4%)

simplify303.0ms (2.1%)

localize310.0ms (2.1%)

series149.0ms (1%)

simplify345.0ms (2.4%)

rewrite509.0ms (3.5%)

eval590.0ms (4%)

prune167.0ms (1.1%)

simplify350.0ms (2.4%)

localize257.0ms (1.8%)

series51.0ms (0.3%)

simplify268.0ms (1.8%)

rewrite373.0ms (2.6%)

eval86.0ms (0.6%)

prune166.0ms (1.1%)

simplify232.0ms (1.6%)

localize292.0ms (2%)

series46.0ms (0.3%)

simplify340.0ms (2.3%)

rewrite297.0ms (2%)

eval97.0ms (0.7%)

prune157.0ms (1.1%)

regimes44.0ms (0.3%)

regimes76.0ms (0.5%)

regimes56.0ms (0.4%)

regimes32.0ms (0.2%)

regimes25.0ms (0.2%)

regimes28.0ms (0.2%)

regimes23.0ms (0.2%)

regimes22.0ms (0.2%)

regimes19.0ms (0.1%)

regimes16.0ms (0.1%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes12.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify16.0ms (0.1%)

soundness1.5s (10.1%)

preprocess186.0ms (1.3%)

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