Metrics for 2tan (problem 3.3.2)

analyze41.0ms (0.3%)

Memory

36.2MiB live, 73.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.0s (44%)

Memory

-132.5MiB live, 7 907.1MiB allocated

Samples

4.1s	26 155×	0	invalid
805.0ms	5 569×	0	valid
526.0ms	2 687×	1	valid

Precisions

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

const: 925.0ms (24.3% of total)

ival-tan: 628.0ms (16.5% of total)

ival-<: 391.0ms (10.3% of total)

ival-sub: 387.0ms (10.2% of total)

ival-fabs: 373.0ms (9.8% of total)

ival-<=: 324.0ms (8.5% of total)

ival-mult: 299.0ms (7.9% of total)

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

ival-and: 97.0ms (2.6% of total)

adjust: 75.0ms (2% of total)

exact: 42.0ms (1.1% of total)

ival-assert: 11.0ms (0.3% of total)

Bogosity

preprocess26.0ms (0.2%)

Memory

10.0MiB live, 49.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

explain98.0ms (0.6%)

Memory

31.3MiB live, 108.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
225	2	(1.0842137292829784e-97 7.629361084465591e-100)	9	(-1.0729840744805937e-269 1.1497784130418687e-271)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
3	0	-	1	(-52.78186261370149 1.2474501562079149e-14)	`(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	218	12
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	2	1

Confusion

	Predicted +	Predicted -
+	217	9
-	2	28

Precision

0.9908675799086758

Recall

0.9601769911504425

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	217	9	0
-	2	3	25

Precision?

0.9783549783549783

Recall?

1.0

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

19.0ms	154×	1	valid
17.0ms	352×	0	valid
3.0ms	4×	2	valid
1.0ms	2×	3	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-tan: 12.0ms (56.3% of total)

adjust: 4.0ms (18.8% of total)

ival-add: 3.0ms (14.1% of total)

ival-sub: 3.0ms (14.1% of total)

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

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

eval0.0ms (0%)

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

prune3.0ms (0%)

Memory

-38.9MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize27.0ms (0.2%)

Memory

-0.2MiB live, 37.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(tan.f64 x)
✓	accuracy	99.8%	(tan.f64 (+.f64 x eps))
✓	accuracy	64.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

10.0ms	77×	1	valid
8.0ms	176×	0	valid
1.0ms	2×	2	valid
0.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-tan: 8.0ms (61.6% of total)

adjust: 2.0ms (15.4% of total)

ival-add: 2.0ms (15.4% of total)

ival-sub: 1.0ms (7.7% of total)

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

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

series11.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB 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	eps	@	0	(- (tan (+ x eps)) (tan x))
2.0ms	eps	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	0	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	-inf	(- (tan (+ x eps)) (tan x))

simplify373.0ms (2.4%)

Memory

-15.3MiB live, 458.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1351
1	464	1285
2	1534	1274
3	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 (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 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (sin.f64 x) (cos.f64 x)))) (-.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))) (+.f64 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/315 binary64) #s(literal 2/15 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite304.0ms (1.9%)

Memory

15.8MiB live, 352.9MiB allocated

Algorithm

1×	batch-egg-rewrite

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))

eval39.0ms (0.2%)

Memory: -6.0MiB live, 69.7MiB allocated
Compiler: Compiled 8 701 to 983 computations (88.7% saved)

prune75.0ms (0.5%)

Memory

-11.0MiB live, 107.5MiB allocated

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	316	20	336
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	316	21	337

Accuracy

100.0%

Counts

337 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.3%	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	64.3%	(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)))
	64.0%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 x eps)))
	63.3%	(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))))
	22.1%	(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))
	34.7%	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶	64.1%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	64.1%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x))))
	64.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
▶	64.3%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	64.0%	(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
	36.0%	(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))) (tan.f64 x))
✓	64.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
▶	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
▶	36.0%	(-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (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))))
	99.5%	#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))
▶	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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))
	99.2%	#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))
	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 949 to 478 computations (49.6% saved)

simplify340.0ms (2.1%)

Memory

24.8MiB live, 461.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(tan.f64 x)
✓	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) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓	cost-diff	0	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (-.f64 (+.f64 x eps) x))
✓	cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	cost-diff	384	(-.f64 (+.f64 x eps) x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 x eps))
✓	cost-diff	0	(tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps))))
✓	cost-diff	0	(-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
✓	cost-diff	1728	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
✓	cost-diff	0	#s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(tan.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
✓	cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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 #s(literal 1/6 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))))
✓	cost-diff	5824	(fma.f64 eps (fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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

15 836×	`lower-fma.f32`
15 824×	`lower-fma.f64`
3 536×	`lower-*.f32`
3 524×	`lower-*.f64`
2 558×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	730
0	110	696
1	188	614
2	424	607
3	1197	603
4	4626	603
0	8076	593

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

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

localize313.0ms (2%)

Memory

13.5MiB live, 461.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓	accuracy	100.0%	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	accuracy	100.0%	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	accuracy	64.4%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	accuracy	100.0%	(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	accuracy	100.0%	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	64.2%	(-.f64 (+.f64 x eps) x)
✓	accuracy	99.8%	(tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (-.f64 x eps))
✓	accuracy	64.4%	(-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
✓	accuracy	55.6%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
✓	accuracy	99.8%	(tan.f64 (+.f64 x eps))
✓	accuracy	99.8%	(.f64 #s(literal 1/3 binary64) (.f64 x x))
✓	accuracy	98.8%	#s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x))
✓	accuracy	64.4%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
✓	accuracy	100.0%	(pow.f64 (sin.f64 x) #s(literal 4 binary64))
✓	accuracy	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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	99.8%	(fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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	98.5%	(+.f64 #s(literal 1/6 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))))

Samples

79.0ms	172×	0	valid
68.0ms	77×	1	valid
45.0ms	7×	5	exit

Compiler

Compiled 657 to 61 computations (90.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 159.0ms

ival-tan: 46.0ms (28.9% of total)

ival-mult: 21.0ms (13.2% of total)

ival-div: 20.0ms (12.6% of total)

adjust: 15.0ms (9.4% of total)

ival-add: 14.0ms (8.8% of total)

ival-sub: 9.0ms (5.7% of total)

ival-pow: 9.0ms (5.7% of total)

const: 8.0ms (5% of total)

ival-pow2: 8.0ms (5% of total)

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

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

exact: 1.0ms (0.6% of total)

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

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

series98.0ms (0.6%)

Memory

-15.0MiB live, 156.7MiB allocated

Counts

25 → 528

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 (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 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 #s(literal 1/6 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)))) (patch (+.f64 #s(literal 1/6 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)))) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x))) (patch (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) 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 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)) (patch #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (patch (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) #<representation binary64>) () ())
#s(alt (-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) (patch (-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (patch (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (patch (/.f64 #s(literal 1 binary64) (-.f64 x eps)) #<representation binary64>) () ())
#s(alt (-.f64 (+.f64 x eps) x) (patch (-.f64 (+.f64 x eps) x) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())
#s(alt (sin.f64 (-.f64 (+.f64 x eps) x)) (patch (sin.f64 (-.f64 (+.f64 x eps) x)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) (patch (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (patch (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) #<representation binary64>) () ())
#s(alt (+.f64 (tan.f64 x) (tan.f64 eps)) (patch (+.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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 (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 #s(literal 1/6 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 (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 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/3 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x 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 (.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>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 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>) () ())) ())
#s(alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf 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 (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf 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 (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2) (taylor inf 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 (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/3 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/3 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#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>) () ())) ())
#s(alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (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)) (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>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos (- eps (* -1 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (cos 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>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (taylor 0 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 (+ 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>) () ())) ())
#s(alt (cos eps) (taylor 0 x) (#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 (+ (cos eps) (* -1 (* x (sin eps)))) (taylor 0 x) (#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 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) (taylor 0 x) (#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 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) (taylor 0 x) (#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 (* (cos x) (cos (+ eps x))) (taylor inf x) (#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 (* (cos x) (cos (+ eps x))) (taylor inf x) (#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 (* (cos x) (cos (+ eps x))) (taylor inf x) (#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 (* (cos x) (cos (+ eps x))) (taylor inf x) (#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 (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#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 (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#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 (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#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 (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#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 (pow (cos x) 2) (taylor 0 eps) (#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 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) (taylor 0 eps) (#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 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (/ (* 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

132 calls:

Time	Variable		Point	Expression
12.0ms	x	@	0	(* (tan x) (tan eps))
10.0ms	x	@	inf	(+ (* eps (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)
9.0ms	eps	@	inf	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
4.0ms	x	@	inf	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
4.0ms	x	@	-inf	(+ (* eps (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)

simplify356.0ms (2.3%)

Memory

23.5MiB live, 490.0MiB allocated

Algorithm

1×	egg-herbie

Rules

8 340×	`lower-fma.f64`
8 340×	`lower-fma.f32`
5 338×	`lower-*.f64`
5 338×	`lower-*.f32`
4 278×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	693	10187
1	2205	9882
2	7234	9759
0	8026	9430

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 489

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))))))
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(+ (* 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)))
(pow x 4)
(* (pow x 4) (+ 1 (* -2/3 (pow x 2))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3))))
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3))))
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow 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)))
(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))))
(/ (* 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 x (.f64 x (fma.f64 x (.f64 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 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -17/135 binary64) #s(literal -2/9 binary64))) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(* 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 (+.f64 (fma.f64 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))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.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)))))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+.f64 (fma.f64 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))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.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)))))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (.f64 eps (*.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)) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.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))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps 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))) (+.f64 (+.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)))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 eps (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))
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(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (.f64 #s(literal 1/6 binary64) (.f64 x (sin.f64 eps)))) (sin.f64 (neg.f64 eps))) (cos.f64 eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (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))
(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 x (.f64 (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 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (*.f64 (cos.f64 x) eps) (neg.f64 (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (*.f64 (sin.f64 x) (cos.f64 x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) (.f64 (cos.f64 x) eps)) (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(/ (* 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 x x) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps)) (/.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 (sin.f64 eps) #s(literal 2/15 binary64)) (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 (.f64 x x) #s(literal 17/315 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (.f64 (sin.f64 eps) #s(literal 2/15 binary64)) (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 #s(literal 1/3 binary64) (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.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 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (.f64 eps eps) #s(literal 2/15 binary64)) (/.f64 (*.f64 #s(literal 1/3 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)))

rewrite351.0ms (2.2%)

Memory

-7.2MiB live, 424.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 612×	`lower-*.f32`
4 600×	`lower-*.f64`
4 344×	`lower-fma.f32`
4 332×	`lower-fma.f64`
3 492×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	450
0	110	395
1	479	289
2	4357	283
0	9325	273

Stop Event

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

Counts

25 → 654

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

eval244.0ms (1.5%)

Memory: 16.9MiB live, 338.3MiB allocated
Compiler: Compiled 44 366 to 2 935 computations (93.4% saved)

prune165.0ms (1%)

Memory

23.0MiB live, 258.2MiB allocated

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	1 329	12	1 341
Fresh	14	1	15
Picked	4	1	5
Done	0	1	1
Total	1 347	15	1 362

Accuracy

100.0%

Counts

1 362 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.3%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
	99.8%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	99.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	64.3%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	64.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
	99.8%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 (*.f64 eps eps) (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 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
	99.5%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
▶	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	99.2%	#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	98.9%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.9%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
	98.0%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x eps))) eps))
▶	98.0%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.0%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)) eps))))

Compiler

Compiled 557 to 296 computations (46.9% saved)

simplify363.0ms (2.3%)

Memory

-9.6MiB live, 514.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(tan.f64 eps)
✓	cost-diff	0	(fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)))
✓	cost-diff	320	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))))
✓	cost-diff	0	(fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)
✓	cost-diff	0	#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps))
✓	cost-diff	0	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))

Rules

14 514×	`lower-fma.f32`
14 496×	`lower-fma.f64`
3 180×	`lower-*.f32`
3 170×	`lower-*.f64`
2 910×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	806
0	112	806
1	220	720
2	513	711
3	1247	705
4	3450	705
5	6798	705
0	8308	680

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps))
(fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)
eps
(.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(*.f64 eps eps)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
(*.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
eps
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
x
#s(literal 2 binary64)
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))
(tan.f64 eps)
eps
(neg.f64 (tan.f64 x))
(tan.f64 x)
x
(+.f64 (tan.f64 x) (tan.f64 eps))

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

localize309.0ms (2%)

Memory

-20.9MiB live, 413.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(neg.f64 (tan.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)))
✓	accuracy	99.9%	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	accuracy	64.3%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
✓	accuracy	100.0%	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
✓	accuracy	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	accuracy	99.8%	(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	99.8%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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	99.8%	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
✓	accuracy	97.9%	#s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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	100.0%	(*.f64 eps eps)
✓	accuracy	99.8%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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	99.8%	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
✓	accuracy	53.6%	#s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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	100.0%	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	99.8%	(.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))))
✓	accuracy	99.4%	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))

Samples

103.0ms	175×	0	valid
91.0ms	78×	1	valid
7.0ms	1×	3	valid
3.0ms	2×	2	valid

Compiler

Compiled 559 to 71 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 176.0ms

ival-mult: 29.0ms (16.5% of total)

ival-pow: 26.0ms (14.8% of total)

ival-add: 26.0ms (14.8% of total)

const: 21.0ms (12% of total)

adjust: 20.0ms (11.4% of total)

ival-div: 18.0ms (10.3% of total)

ival-tan: 16.0ms (9.1% of total)

ival-pow2: 6.0ms (3.4% of total)

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

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

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

ival-neg: 1.0ms (0.6% of total)

exact: 1.0ms (0.6% of total)

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

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

series72.0ms (0.5%)

Memory

-10.9MiB live, 79.8MiB allocated

Counts

26 → 516

Calls

Call 1

Inputs
#s(alt (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (patch #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps) (patch (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (patch (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) #<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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))) (patch #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (patch (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #<representation binary64>) () ())
#s(alt (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))) (patch (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))) #<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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) #<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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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) (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)))) (patch #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch #s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (patch (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) (patch (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (tan.f64 eps) (patch (tan.f64 eps) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x 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 (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())
#s(alt (+.f64 (tan.f64 x) (tan.f64 eps)) (patch (+.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())
#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())

Outputs
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) (taylor 0 x) (#s(alt (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())) ())
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#s(alt (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#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 (* (cos x) (cos (- eps (* -1 x)))) (taylor -inf x) (#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 (pow (cos x) 2) (taylor 0 eps) (#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 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) (taylor 0 eps) (#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 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (patch (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #<representation binary64>) () ())) ())
#s(alt (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (+ eps x))) (taylor inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (* (cos x) (cos (- x (* -1 eps)))) (taylor -inf eps) (#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 (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (/ (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 (/ (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 (* 1/3 (pow x 2)))) (/ (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 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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 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 (/ (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 (* 1/3 (pow eps 2)))) (/ (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 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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) (cos eps)) (/ (sin x) (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 (* -1 x) (taylor 0 x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -1/3 (pow x 2)) 1)) (taylor 0 x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (- (* -2/15 (pow x 2)) 1/3)) 1)) (taylor 0 x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/315 (pow x 2)) 2/15)) 1/3)) 1)) (taylor 0 x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (neg.f64 (tan.f64 x)) (patch (neg.f64 (tan.f64 x)) #<representation binary64>) () ())) ())

Calls

129 calls:

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

simplify377.0ms (2.4%)

Memory

22.4MiB live, 491.3MiB allocated

Algorithm

1×	egg-herbie

Rules

9 864×	`lower-fma.f64`
9 864×	`lower-fma.f32`
5 616×	`lower-*.f64`
5 616×	`lower-*.f32`
4 402×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	655	11346
1	2090	11035
2	7040	10834
0	8312	10432

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 512

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* 1/120 (pow eps 5))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))
(* 1/120 (pow eps 4))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 4))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (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)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(+ (/ (sin 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))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
1
(+ 1 (/ (* eps (sin x)) (cos x)))
(+ 1 (* eps (- (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) (* -1 (/ (sin x) (cos x))))))
(+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))) (* -1/3 (/ (sin x) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (sin x) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
1
(+ 1 (/ (* x (sin eps)) (cos eps)))
(+ 1 (* x (- (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)) (* -1 (/ (sin eps) (cos eps))))))
(+ 1 (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (sin eps) (cos eps))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ 1 (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
1
(+ 1 (* -1 (/ (* eps (sin x)) (cos x))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x))))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x))))))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
1
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* -1/3 (/ (sin eps) (cos eps))) (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))))))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(* -1/6 eps)
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(* 1/120 (pow eps 3))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(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)))
(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))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(/ (sin eps) (cos eps))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(* -1 x)
(* x (- (* -1/3 (pow x 2)) 1))
(* x (- (* (pow x 2) (- (* -2/15 (pow x 2)) 1/3)) 1))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/315 (pow x 2)) 2/15)) 1/3)) 1))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))
(* -1 (/ (sin x) (cos x)))

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

rewrite510.0ms (3.2%)

Memory

24.3MiB live, 537.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 858×	`lower-fma.f32`
5 840×	`lower-fma.f64`
5 202×	`lower-*.f32`
5 192×	`lower-*.f64`
2 294×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	750
0	112	739
1	555	573
2	5097	573
0	8236	540

Stop Event

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

Counts

26 → 385

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps))
(fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)
(.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)))
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(tan.f64 eps)
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))
(cos.f64 (+.f64 x eps))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(*.f64 eps eps)
(+.f64 (tan.f64 x) (tan.f64 eps))
(neg.f64 (tan.f64 x))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)))) #s(literal -1 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps))))
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(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)) (cos.f64 x))))
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(/.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(pow.f64 (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)) (cos.f64 x))) #s(literal -1 binary64))
(.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
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(.f64 (neg.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))))
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(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps))) #s(literal -1 binary64)))
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(.f64 (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)) (+.f64 (cos.f64 (+.f64 x (+.f64 x eps))) (cos.f64 (-.f64 x (+.f64 x eps))))) #s(literal 2 binary64))
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(+.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64))))
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(fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)) (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)))))
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal -1 binary64)) (+.f64 (pow.f64 (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) #s(literal -1 binary64))))
(/.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (neg.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64))) (.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (tan.f64 x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (tan.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal -1 binary64)) (+.f64 (pow.f64 (*.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(*.f64 (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)))))))
(.f64 (+.f64 (pow.f64 (.f64 (tan.f64 eps) (neg.f64 (tan.f64 x))) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal -1 binary64))))
(tan.f64 eps)
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 eps) (sin.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps)))
(pow.f64 (/.f64 (cos.f64 eps) (sin.f64 eps)) #s(literal -1 binary64))
(*.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))
(+.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps #s(literal -1/6 binary64)))
(+.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps))))
(fma.f64 eps #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (.f64 eps (*.f64 eps eps))))
(fma.f64 eps (.f64 eps (.f64 eps #s(literal 1/120 binary64))) (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 (.f64 eps eps) (.f64 eps #s(literal 1/120 binary64)) (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps)) (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal 1/120 binary64) (.f64 eps (*.f64 eps eps))))
(fma.f64 (.f64 eps (.f64 eps #s(literal 1/120 binary64))) eps (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/120 binary64) (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 (.f64 eps #s(literal 1/120 binary64)) (.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64)))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728000 binary64))) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/216 binary64))) (fma.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps))) (-.f64 (.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps #s(literal -1/6 binary64))) (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps))) (*.f64 eps #s(literal -1/6 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps #s(literal -1/6 binary64)))) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps #s(literal -1/6 binary64))))
(/.f64 (.f64 eps (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64))) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))
(/.f64 (.f64 eps (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64))) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal 1/6 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/1728000 binary64)) #s(literal -1/216 binary64)) eps) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/14400 binary64) (-.f64 #s(literal 1/36 binary64) (.f64 (*.f64 eps eps) #s(literal -1/720 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/14400 binary64) #s(literal -1/36 binary64)) eps) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal 1/6 binary64)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)
(+.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (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 x) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 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 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))) (cos.f64 (-.f64 x eps)))
(/.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 x (-.f64 eps 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))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(pow.f64 eps #s(literal 2 binary64))
(*.f64 eps eps)
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(+.f64 (tan.f64 x) (tan.f64 eps))
(+.f64 (.f64 #s(literal 1 binary64) (tan.f64 x)) (.f64 #s(literal 1 binary64) (tan.f64 eps)))
(+.f64 (.f64 #s(literal 1 binary64) (tan.f64 eps)) (.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (.f64 (tan.f64 eps) #s(literal 1 binary64)) (.f64 (tan.f64 x) #s(literal 1 binary64)))
(+.f64 (.f64 (tan.f64 x) #s(literal 1 binary64)) (.f64 (tan.f64 eps) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 eps))
(fma.f64 #s(literal 1 binary64) (tan.f64 eps) (*.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(fma.f64 (tan.f64 eps) #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(literal 1 binary64)))
(fma.f64 (tan.f64 x) #s(literal 1 binary64) (*.f64 (tan.f64 eps) #s(literal 1 binary64)))
(fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))
(/.f64 (sin.f64 (+.f64 x eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 eps) (tan.f64 x)))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (tan.f64 x) (tan.f64 eps))))
(/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (tan.f64 eps) (tan.f64 x)))
(pow.f64 (/.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (tan.f64 eps) (tan.f64 x)))
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 1 binary64))
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 x) (tan.f64 eps))))
(+.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 x)))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
(neg.f64 (tan.f64 x))
(/.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (sin.f64 x)) (cos.f64 x))
(/.f64 (sin.f64 (neg.f64 x)) (cos.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 (tan.f64 x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (tan.f64 x))

eval154.0ms (1%)

Memory: 1.0MiB live, 227.2MiB allocated
Compiler: Compiled 28 557 to 1 783 computations (93.8% saved)

prune167.0ms (1.1%)

Memory

-37.8MiB live, 267.3MiB allocated

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	1 001	19	1 020
Fresh	5	3	8
Picked	3	2	5
Done	1	1	2
Total	1 010	25	1 035

Accuracy

100.0%

Counts

1 035 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.3%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (tan eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps)) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
	99.8%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	100.0%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))))
✓	99.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.5%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))
	98.8%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
	98.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
	52.4%	(/.f64 #s(approx (sin (- (+ x eps) x)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)) (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)))))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
▶	99.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	52.4%	(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps))))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	64.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)))
▶	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
	98.4%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
	98.0%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
	98.5%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)))
▶	98.5%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
	98.9%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
▶	98.0%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
✓	98.0%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.9%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.7%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) #s(literal 1 binary64)) eps))
	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)) eps))

Compiler

Compiled 1 097 to 554 computations (49.5% saved)

simplify416.0ms (2.6%)

Memory

33.6MiB live, 475.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)
✓	cost-diff	0	#s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps))
✓	cost-diff	0	(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))
✓	cost-diff	0	(/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
✓	cost-diff	0	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
✓	cost-diff	128	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
✓	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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64)))))
✓	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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
✓	cost-diff	320	(fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))
✓	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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
✓	cost-diff	0	(.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))))
✓	cost-diff	0	(fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)
✓	cost-diff	0	#s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps))
✓	cost-diff	0	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))))

Rules

15 518×	`lower-fma.f32`
15 502×	`lower-fma.f64`
3 274×	`lower-*.f32`
3 250×	`lower-*.f64`
2 994×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	648
0	128	648
1	238	606
2	485	586
3	1026	572
4	3256	572
5	6565	572
0	8292	550

Stop Event

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

Calls

Call 1

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

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

localize493.0ms (3.1%)

Memory

-21.7MiB live, 248.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
✓	accuracy	100.0%	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	99.9%	(*.f64 eps #s(literal 1/120 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))
✓	accuracy	100.0%	(cos.f64 (+.f64 x x))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
✓	accuracy	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal 1/3 binary64)))
✓	accuracy	99.8%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/3 binary64))
✓	accuracy	52.6%	#s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64)))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 eps (*.f64 x x) eps)
✓	accuracy	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
✓	accuracy	98.9%	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps))
✓	accuracy	100.0%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))))
✓	accuracy	100.0%	(.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps))))
✓	accuracy	99.8%	(.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))))
✓	accuracy	99.4%	(.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))

Samples

180.0ms	77×	1	valid
147.0ms	179×	0	valid

Compiler

Compiled 470 to 82 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 198.0ms

ival-sub: 47.0ms (23.8% of total)

ival-mult: 38.0ms (19.2% of total)

ival-div: 28.0ms (14.2% of total)

ival-add: 23.0ms (11.6% of total)

const: 14.0ms (7.1% of total)

adjust: 13.0ms (6.6% of total)

ival-pow: 9.0ms (4.5% of total)

ival-cos: 8.0ms (4% of total)

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

ival-pow2: 5.0ms (2.5% of total)

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

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

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

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

series102.0ms (0.6%)

Memory

5.9MiB live, 80.8MiB allocated

Counts

28 → 528

Calls

Call 1

Inputs
#s(alt (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps))))) (patch (/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps))))) #<representation binary64>) () ())
#s(alt #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (patch #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps) (patch (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (patch (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (.f64 x x) eps))) (patch #s(approx (/ (sin (- (+ x eps) x)) ( (cos x) (cos (+ x eps)))) #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 (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64)))) (patch (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64)))) #<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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) (patch #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (patch (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (patch #s(approx (/ (sin (- (+ x eps) x)) ( (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) #<representation binary64>) () ())
#s(alt (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (patch (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (patch (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (patch (/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #<representation binary64>) () ())
#s(alt #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (patch #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (patch (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (patch (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))) (patch (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/3 binary64)) (patch (.f64 eps #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps (.f64 eps #s(literal 1/3 binary64))) (patch (.f64 eps (.f64 eps #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/120 binary64)) (patch (.f64 eps #s(literal 1/120 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 x eps)) (patch (cos.f64 (+.f64 x 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>) () ())

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

Calls

132 calls:

Time	Variable		Point	Expression
36.0ms	x	@	-inf	(/ eps (+ 1/2 (* 1/2 (cos (+ x x)))))
2.0ms	eps	@	inf	(/ (sin (- (+ x eps) x)) (* (cos x) (+ (* (cos x) (cos eps)) (* (sin (neg x)) (sin eps)))))
2.0ms	x	@	0	(/ (sin (- (+ x eps) x)) (* (cos x) (+ (* (cos x) (cos eps)) (* (sin (neg x)) (sin eps)))))
1.0ms	x	@	inf	(/ (sin (- (+ x eps) x)) (* (cos x) (+ (* (cos x) (cos eps)) (* (sin (neg x)) (sin eps)))))
1.0ms	x	@	-inf	(/ (sin (- (+ x eps) x)) (* (cos x) (+ (* (cos x) (cos eps)) (* (sin (neg x)) (sin eps)))))

simplify494.0ms (3.1%)

Memory

-0.8MiB live, 559.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 516×	`lower-fma.f64`
9 516×	`lower-fma.f32`
6 846×	`lower-*.f64`
6 846×	`lower-*.f32`
2 866×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	535	8066
1	1666	7816
2	5481	7659
0	8994	7353

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 521

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) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/ eps (pow (cos x) 2))
(* eps (+ (* -1 (/ (* eps (sin (neg x))) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin (neg x)) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (/ (sin (neg x)) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (sin (neg x)) (pow (cos x) 3))) (+ (* 1/2 (/ (sin (neg x)) (pow (cos x) 3))) (/ (* (sin (neg x)) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin (neg x)) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x)))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin (neg x)) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (/ (sin (neg x)) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* 1/120 (pow eps 5))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))
(* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))
(* 1/120 (pow eps 4))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 4))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 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 (+ 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)
(* eps x)
(* eps (+ x (* 1/3 eps)))
(* eps (+ x (* 1/3 eps)))
(* eps (+ x (* 1/3 eps)))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* eps x))
(* eps x)
(* x (+ eps (* 1/3 (/ (pow eps 2) x))))
(* x (+ eps (* 1/3 (/ (pow eps 2) x))))
(* x (+ eps (* 1/3 (/ (pow eps 2) x))))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (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
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(+ 1/2 (* 1/2 (cos (neg (* -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 (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
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 (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))
(/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))
(/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))
(/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))
1/2
(+ 1/2 (* -1 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(* 1/2 (cos (* 2 x)))
(* 1/2 (cos (* 2 x)))
(* 1/2 (cos (* 2 x)))
(* 1/2 (cos (* 2 x)))
(* 1/2 (cos (neg (* -2 x))))
(* 1/2 (cos (neg (* -2 x))))
(* 1/2 (cos (neg (* -2 x))))
(* 1/2 (cos (neg (* -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)))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* 1/120 (pow eps 5))
(* (pow eps 5) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))
(* 1/120 (pow eps 4))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 4))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(* -1/6 eps)
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(* 1/120 (pow eps 3))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(* 1/120 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(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) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(pow (cos x) 2)
(+ (* eps (* (cos x) (sin (neg x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1/2 (* eps (pow (cos x) 2))) (* (cos x) (sin (neg x))))) (pow (cos x) 2))
(+ (* eps (+ (* eps (+ (* -1/2 (pow (cos x) 2)) (* -1/6 (* eps (* (cos x) (sin (neg x))))))) (* (cos x) (sin (neg x))))) (pow (cos x) 2))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 1/3 eps)
(* 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
(+ 1 (* -2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))
(cos (* 2 x))
(cos (* 2 x))
(cos (* 2 x))
(cos (* 2 x))
(cos (neg (* -2 x)))
(cos (neg (* -2 x)))
(cos (neg (* -2 x)))
(cos (neg (* -2 x)))
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 eps)
(* 1/120 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)))
(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))))

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (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 (+.f64 (fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (neg.f64 (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps)))) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (neg.f64 x) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (* -1 (/ (* eps (sin (neg x))) (pow (cos x) 3))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin (neg x)) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (/ (sin (neg x)) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))
(fma.f64 (*.f64 eps eps) (fma.f64 eps (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.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 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (sin (neg x)) (pow (cos x) 3))) (+ (* 1/2 (/ (sin (neg x)) (pow (cos x) 3))) (/ (* (sin (neg x)) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin (neg x)) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x)))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin (neg x)) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (/ (sin (neg x)) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (+.f64 (fma.f64 (neg.f64 eps) (fma.f64 (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.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 (neg.f64 x)) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin eps) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x))))))
(/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
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(* x (+ eps (* 1/3 (/ (pow eps 2) x))))
(.f64 x (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) x) eps))
(* x (+ eps (* 1/3 (/ (pow eps 2) x))))
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(* eps x)
(*.f64 eps x)
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(.f64 x (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) x) eps))
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(.f64 x (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) x) eps))
(* -1 (* x (+ (* -1 eps) (* -1/3 (/ (pow eps 2) x)))))
(.f64 x (fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 eps eps) x) eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
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(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (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 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 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))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (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 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 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))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) (.f64 eps (*.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 eps (.f64 (.f64 eps 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))) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (.f64 eps (cos.f64 x))) (+.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)))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps 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))) (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (/.f64 (sin.f64 x) (.f64 eps (cos.f64 x))))) (+.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)))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps (.f64 eps 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))) (+.f64 (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (/.f64 (sin.f64 x) (.f64 eps (cos.f64 x))))) (+.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)))) (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (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 (pow.f64 eps #s(literal 5 binary64)) (neg.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal -1/120 binary64))))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (-.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps))))) (neg.f64 (pow.f64 eps #s(literal 5 binary64))))
(* -1 (* (pow eps 5) (- (* 1/6 (/ 1 (pow eps 2))) (+ 1/120 (/ 1 (pow eps 4))))))
(.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) (-.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps))))) (neg.f64 (pow.f64 eps #s(literal 5 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(* 1/120 (pow eps 4))
(.f64 #s(literal 1/120 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps)))))
(* 1/120 (pow eps 4))
(.f64 #s(literal 1/120 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (+ 1/120 (/ 1 (pow eps 4))) (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps)))))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(* eps (- (* 1/120 (pow eps 2)) 1/6))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))
(* 1/120 (pow eps 3))
(.f64 eps (.f64 eps (*.f64 eps #s(literal 1/120 binary64))))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- 1/120 (* 1/6 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps)))))
(* 1/120 (pow eps 3))
(.f64 eps (.f64 eps (*.f64 eps #s(literal 1/120 binary64))))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(.f64 (neg.f64 eps) (.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal -1/120 binary64))))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(.f64 (neg.f64 eps) (.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal -1/120 binary64))))
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 (pow eps 2))) 1/120)))
(.f64 (neg.f64 eps) (.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps eps)) #s(literal -1/120 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 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(fma.f64 x (-.f64 (.f64 x (-.f64 (.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64)) (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (* -1 x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* eps (* (cos x) (sin (neg x)))) (pow (cos x) 2))
(fma.f64 eps (*.f64 (cos.f64 x) (sin.f64 (neg.f64 x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1/2 (* eps (pow (cos x) 2))) (* (cos x) (sin (neg x))))) (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) (sin.f64 (neg.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* eps (+ (* -1/2 (pow (cos x) 2)) (* -1/6 (* eps (* (cos x) (sin (neg x))))))) (* (cos x) (sin (neg x))))) (pow (cos x) 2))
(fma.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) (.f64 #s(literal 1/6 binary64) (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) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* (cos x) (+ (* (cos eps) (cos x)) (* (sin eps) (sin (neg x)))))
(.f64 (cos.f64 x) (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 2/3 binary64)) #s(literal -2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -4/45 binary64) #s(literal 2/3 binary64)) #s(literal -2 binary64)) #s(literal 1 binary64))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 x #s(literal -2 binary64)))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 binary64))
(* 1/120 eps)
(*.f64 eps #s(literal 1/120 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 #s(literal -1/2 binary64) (.f64 (cos.f64 eps) x)) (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 x (-.f64 (.f64 x (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x)))) (sin.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 (-.f64 (.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))) (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))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(fma.f64 x (-.f64 (.f64 x (-.f64 (.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64)) (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 eps (*.f64 (cos.f64 x) (sin.f64 (neg.f64 x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 eps (fma.f64 eps (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) (sin.f64 (neg.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 (.f64 eps (cos.f64 x)) (.f64 #s(literal 1/6 binary64) (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)))

rewrite405.0ms (2.6%)

Memory

11.4MiB live, 606.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 962×	`lower-*.f32`
4 940×	`lower-*.f64`
4 766×	`lower-fma.f32`
4 750×	`lower-fma.f64`
2 250×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	577
0	128	583
1	593	441
2	4906	441
0	8181	416

Stop Event

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

Counts

28 → 467

Calls

Call 1

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

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

eval113.0ms (0.7%)

Memory: 5.0MiB live, 201.6MiB allocated
Compiler: Compiled 27 393 to 1 670 computations (93.9% saved)

prune188.0ms (1.2%)

Memory

0.4MiB live, 213.0MiB allocated

Pruning

28 alts after pruning (23 fresh and 5 done)

	Pruned	Kept	Total
New	979	9	988
Fresh	3	14	17
Picked	3	2	5
Done	0	3	3
Total	985	28	1 013

Accuracy

100.0%

Counts

1 013 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.3%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (tan eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps)) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
✓	100.0%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))))
✓	99.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.5%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))
	98.8%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
	98.9%	(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
	52.4%	(/.f64 #s(approx (sin (- (+ x eps) x)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)) (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)))))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	52.4%	(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps) (fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (neg.f64 eps))))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.8%	(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.5%	(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	21.6%	(/.f64 #s(approx (sin (- (+ x eps) x)) #s(approx (+ (* eps (* eps (* eps (+ (* (* eps eps) 1/120) -1/6)))) eps) (.f64 (pow.f64 eps #s(literal 5 binary64)) (+.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -1/6 binary64) (.f64 eps eps))))))) (.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))))
✓	64.1%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	63.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) eps)))
	99.2%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
	98.4%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
	98.0%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
	98.5%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)))
✓	98.5%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
	6.5%	#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* eps (* x x)) eps) (.f64 eps (.f64 x x)))))
	98.9%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
✓	98.0%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.9%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.7%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
	98.0%	#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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps x) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
	98.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) #s(literal 1 binary64)) eps))
	98.0%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)) eps))
	50.5%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (.f64 (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps)))))

Compiler

Compiled 1 940 to 596 computations (69.3% saved)

regimes62.0ms (0.4%)

Memory

-19.5MiB live, 56.4MiB allocated

Counts

61 → 1

Calls

Call 1

Inputs
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* eps (* x x)) eps) (.f64 eps (.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps x) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))
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(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 #s(approx (sin (- (+ x eps) x)) (.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps) (fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (neg.f64 eps))))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (tan eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps)) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps (-.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))) (+.f64 #s(literal 1/6 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 (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

(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (*.f64 (cos.f64 x) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 eps)))))

Calls

3 calls:

27.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
17.0ms	x
15.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes45.0ms (0.3%)

Memory

19.5MiB live, 59.0MiB allocated

Counts

52 → 1

Calls

Call 1

Inputs
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* eps (* x x)) eps) (.f64 eps (.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps x) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)))
#s(approx (- (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) #s(literal 1 binary64)) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (.f64 (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps)))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) #s(approx (sin (- (+ x eps) x)) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) 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)))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps))))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 (.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps) (fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) (neg.f64 eps))))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 (-.f64 (+.f64 x eps) x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)) (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (neg.f64 eps)))))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (-.f64 (+.f64 x eps) x))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 eps (sin.f64 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 (* (tan x) (tan eps)))) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (tan eps) (fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps)) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.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)))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (tan.f64 x)))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (fma.f64 eps (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Outputs

(/.f64 #s(approx (sin (- (+ x eps) x)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))

Calls

3 calls:

17.0ms	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)

regimes30.0ms (0.2%)

Memory

6.0MiB live, 42.0MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* eps (* x x)) eps) (.f64 eps (.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps x) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)))
#s(approx (- (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) #s(literal 1 binary64)) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (.f64 (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps)))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/6 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))) (tan.f64 x))

Outputs

(/.f64 #s(approx (sin (- (+ x eps) x)) (*.f64 #s(approx (+ (* (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`eps`
99.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.2%)

Memory

6.1MiB live, 44.9MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* eps (* x x)) eps) (.f64 eps (.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps x) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)))
#s(approx (- (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) #s(literal 1 binary64)) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (.f64 (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps)))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (tan.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (tan.f64 x))

Outputs
(/.f64 #s(approx (sin (- (+ x eps) x)) (.f64 #s(approx (+ ( (* eps eps) (+ (* eps (* eps 1/120)) -1/6)) 1) #s(literal 1 binary64)) 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	eps
7.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.1%)

Memory

0.4MiB live, 39.5MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* eps (* x x)) eps) (.f64 eps (.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* eps x) (* eps (* eps 1/3))) (*.f64 eps x))) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 eps (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 1 binary64)) eps))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 #s(literal 1/3 binary64) (.f64 eps eps) (.f64 x eps))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 eps #s(approx (+ (* eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 eps x (.f64 eps (.f64 eps #s(literal 1/3 binary64))))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps) (fma.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)) eps))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (*.f64 eps #s(literal 2/3 binary64)) eps) eps)))
#s(approx (- (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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)) (.f64 (+.f64 #s(approx (+ ( eps (+ (* eps (- (/ (+ (pow (sin x) 2) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (+ 1/6 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 eps (.f64 eps #s(literal 4/3 binary64)) #s(literal 1 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) #s(literal 1 binary64)) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) eps) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (.f64 (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) 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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) (neg.f64 eps)))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x x)) x)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ x eps) x)) (fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #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 (/ (sin (- (+ x eps) x)) (* (cos x) (cos (+ x eps)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

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

Calls

3 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`
99.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.1%)

Memory

-17.5MiB live, 24.6MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

8.0ms	eps
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

22.2MiB live, 22.2MiB allocated

Counts

14 → 1

Calls

Call 1

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

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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-18.9MiB live, 20.2MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

#s(approx (- (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 (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) -1/2))))) (/ (+ (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:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

regimes5.0ms (0%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

Calls

3 calls:

2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`eps`
98.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

-30.6MiB live, 8.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
1.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms	eps

Results

Accuracy	Segments	Branch
6.5%	1	`eps`
6.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
6.5%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	664
1	166	664
2	168	664
3	169	664

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (9.3%)

Memory

24.8MiB live, 1 058.5MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
9 864×	`lower-fma.f64`
9 864×	`lower-fma.f32`
9 516×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	655	11346
1	2090	11035
2	7040	10834
0	8312	10432
0	157	1351
1	464	1285
2	1534	1274
3	5949	1242
0	8534	1195
0	85	577
0	128	583
1	593	441
2	4906	441
0	8181	416
0	535	8066
1	1666	7816
2	5481	7659
0	8994	7353
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	693	10187
1	2205	9882
2	7234	9759
0	8026	9430
0	75	750
0	112	739
1	555	573
2	5097	573
0	8236	540

Stop Event

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

Compiler

Compiled 657 to 339 computations (48.4% saved)

preprocess90.0ms (0.6%)

Memory: -6.5MiB live, 189.1MiB allocated
Compiler: Compiled 444 to 178 computations (59.9% 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

analyze41.0ms (0.3%)

sample7.0s (44%)

preprocess26.0ms (0.2%)

explain98.0ms (0.6%)

eval0.0ms (0%)

prune3.0ms (0%)

simplify9.0ms (0.1%)

localize27.0ms (0.2%)

series11.0ms (0.1%)

simplify373.0ms (2.4%)

rewrite304.0ms (1.9%)

eval39.0ms (0.2%)

prune75.0ms (0.5%)

simplify340.0ms (2.1%)

localize313.0ms (2%)

series98.0ms (0.6%)

simplify356.0ms (2.3%)

rewrite351.0ms (2.2%)

eval244.0ms (1.5%)

prune165.0ms (1%)

simplify363.0ms (2.3%)

localize309.0ms (2%)

series72.0ms (0.5%)

simplify377.0ms (2.4%)

rewrite510.0ms (3.2%)

eval154.0ms (1%)

prune167.0ms (1.1%)

simplify416.0ms (2.6%)

localize493.0ms (3.1%)

series102.0ms (0.6%)

simplify494.0ms (3.1%)

rewrite405.0ms (2.6%)

eval113.0ms (0.7%)

prune188.0ms (1.2%)

regimes62.0ms (0.4%)

regimes45.0ms (0.3%)

regimes30.0ms (0.2%)

regimes25.0ms (0.2%)

regimes23.0ms (0.1%)

regimes20.0ms (0.1%)

regimes14.0ms (0.1%)

regimes13.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes5.0ms (0%)

simplify11.0ms (0.1%)

soundness1.5s (9.3%)

preprocess90.0ms (0.6%)

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