Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze45.0ms (0.3%)

Memory

16.7MiB live, 95.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.7s (48.7%)

Memory

-174.7MiB live, 7 954.7MiB allocated

Samples

3.4s	26 447×	0	invalid
720.0ms	5 425×	0	valid
699.0ms	2 831×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.3s

const: 705.0ms (21.3% of total)

ival-tan: 662.0ms (20% of total)

ival-sub: 385.0ms (11.6% of total)

ival-mult: 322.0ms (9.7% of total)

ival-<=: 264.0ms (8% of total)

ival-fabs: 243.0ms (7.3% of total)

ival-add: 240.0ms (7.3% of total)

ival-<: 205.0ms (6.2% of total)

ival-and: 136.0ms (4.1% of total)

adjust: 86.0ms (2.6% of total)

exact: 47.0ms (1.4% of total)

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

Bogosity

explain132.0ms (1%)

Memory

13.6MiB live, 90.4MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`	cancellation	219	5
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	216	4
-	3	33

Precision

0.9863013698630136

Recall

0.9818181818181818

Confusion?

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

Precision?

0.9776785714285714

Recall?

0.9954545454545455

Freqs

test

number	freq
0	37
1	218
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms	342×	0	valid
23.0ms	6×	3	valid
16.0ms	162×	1	valid
3.0ms	2×	2	valid

Compiler

Compiled 49 to 22 computations (55.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-tan: 33.0ms (76.2% of total)

adjust: 4.0ms (9.2% of total)

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

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

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

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

preprocess22.0ms (0.2%)

Memory

17.4MiB live, 17.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify55.0ms (0.4%)

Memory

-33.1MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tan.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize36.0ms (0.3%)

Memory

26.3MiB live, 26.3MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

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

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-tan: 16.0ms (74.5% of total)

adjust: 2.0ms (9.3% of total)

ival-add: 2.0ms (9.3% of total)

ival-sub: 2.0ms (9.3% of total)

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

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

series11.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB 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))

simplify300.0ms (2.2%)

Memory

-9.1MiB live, 105.0MiB 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 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/6 binary64)))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(/ (sin 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))

rewrite219.0ms (1.6%)

Memory

17.0MiB live, 132.9MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 259

Calls

Call 1

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

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

eval51.0ms (0.4%)

Memory: -19.6MiB live, 100.8MiB allocated
Compiler: Compiled 8 701 to 985 computations (88.7% saved)

prune58.0ms (0.4%)

Memory

-2.6MiB live, 114.0MiB allocated

Pruning

17 alts after pruning (16 fresh and 1 done)

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

Accuracy

100.0%

Counts

337 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.7%	(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x)))
	62.5%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
	61.5%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
	62.5%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	62.5%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
	62.6%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	62.5%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
▶	62.6%	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
▶	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
▶	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 751 to 382 computations (49.1% saved)

simplify177.0ms (1.3%)

Memory

7.6MiB live, 245.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize281.0ms (2%)

Memory

18.8MiB live, 406.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (tan.f64 eps) (tan.f64 x))
accuracy	0.01953125	(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy	0.10775375976844201	(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))
accuracy	23.918482892439503	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
accuracy	0.015625	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.05097464160568397	(cos.f64 (+.f64 eps x))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))))
accuracy	23.96972852167959	(-.f64 (+.f64 eps x) x)
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(/.f64 (sin.f64 x) (cos.f64 x))
accuracy	0.07219329735525831	(tan.f64 (+.f64 x eps))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy	0.0078125	(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))
accuracy	0.07219329735525831	(tan.f64 (+.f64 x eps))
accuracy	0.9033645080441755	#s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
accuracy	23.918482892439503	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
accuracy	0.033535009768442016	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.109375	(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.9889450195368841	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

82.0ms	88×	1	valid
77.0ms	162×	0	valid
20.0ms	4×	3	valid
11.0ms	2×	2	valid

Compiler

Compiled 709 to 63 computations (91.1% saved)

Precisions

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

ival-tan: 27.0ms (17.7% of total)

ival-mult: 24.0ms (15.7% of total)

ival-div: 18.0ms (11.8% of total)

ival-add: 17.0ms (11.1% of total)

adjust: 16.0ms (10.5% of total)

const: 10.0ms (6.6% of total)

ival-sub: 10.0ms (6.6% of total)

ival-pow: 10.0ms (6.6% of total)

ival-pow2: 10.0ms (6.6% of total)

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

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

exact: 1.0ms (0.7% of total)

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

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

series101.0ms (0.7%)

Memory

-18.4MiB live, 140.2MiB allocated

Counts

25 → 516

Calls

Call 1

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

Outputs
#s(alt -1/2 (taylor 0 x) (#s(alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/3 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 4/3 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) (taylor 0 x) (#s(alt (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor inf x) (#s(alt (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf eps) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2)) (taylor 0 x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (* eps (sin x)) (cos x)) (taylor 0 eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<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 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<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 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<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 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf eps) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* x (sin eps)) (cos eps)) (taylor 0 x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<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 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<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 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<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 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 eps) (tan.f64 x)) (patch (.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())) ())

Calls

129 calls:

Time	Variable		Point	Expression
10.0ms	eps	@	-inf	(- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (tan x))
9.0ms	x	@	0	(+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps)
6.0ms	x	@	-inf	(+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps)
4.0ms	x	@	-inf	(- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (tan x))
3.0ms	x	@	inf	(+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps)

simplify259.0ms (1.9%)

Memory

42.9MiB live, 271.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 484

Calls

Call 1

Inputs
-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)
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin eps) (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)))
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x
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eps
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(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (sin eps) (cos eps))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (sin eps) (cos eps)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))))
(/ (sin 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)))
(/ (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)))
(* 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 (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))))))
(pow x 3)
(* (pow x 3) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
1
(+ 1 (* 1/3 (pow x 2)))
(+ 1 (* 1/3 (pow x 2)))
(+ 1 (* 1/3 (pow x 2)))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos 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 (- (* -1/2 (* 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)))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* 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)))
(/ (* 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)))

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

rewrite216.0ms (1.6%)

Memory

-6.0MiB live, 222.0MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

25 → 692

Calls

Call 1

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

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

eval258.0ms (1.9%)

Memory: 1.6MiB live, 327.0MiB allocated
Compiler: Compiled 60 779 to 3 995 computations (93.4% saved)

prune162.0ms (1.2%)

Memory

16.9MiB live, 260.3MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

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

Accuracy

100.0%

Counts

1 448 → 13

Alt Table

Click to see full alt table

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

Compiler

Compiled 527 to 290 computations (45% saved)

simplify148.0ms (1.1%)

Memory

-29.6MiB live, 134.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

12 088×	`lower-fma.f32`
12 078×	`lower-fma.f64`
3 570×	`lower-*.f32`
3 562×	`lower-*.f64`
2 900×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	784
0	100	778
1	172	690
2	421	678
3	1516	678
4	3876	678
0	8136	660

Stop Event

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

Calls

Call 1

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

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

localize244.0ms (1.8%)

Memory

29.3MiB live, 257.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps))
accuracy	0.015625	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.05097464160568397	(cos.f64 (+.f64 eps x))
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps))))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.01171875	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.13671875	(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	1.2060271157130906	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
accuracy	0.00390625	(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
accuracy	0.17530740025640998	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
accuracy	0.17578125	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	31.424916395330225	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.01171875	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.015625	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.05097464160568397	(cos.f64 (+.f64 eps x))

Samples

91.0ms	171×	0	valid
70.0ms	81×	1	valid
4.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 534 to 65 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 138.0ms

ival-add: 27.0ms (19.6% of total)

ival-div: 26.0ms (18.9% of total)

ival-mult: 22.0ms (16% of total)

adjust: 13.0ms (9.4% of total)

const: 12.0ms (8.7% of total)

ival-pow: 9.0ms (6.5% of total)

ival-sin: 7.0ms (5.1% of total)

ival-pow2: 6.0ms (4.4% of total)

ival-sub: 5.0ms (3.6% of total)

ival-cos: 5.0ms (3.6% of total)

ival-tan: 4.0ms (2.9% of total)

exact: 1.0ms (0.7% of total)

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

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

series51.0ms (0.4%)

Memory

-5.6MiB live, 44.3MiB allocated

Counts

20 → 432

Calls

Call 1

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

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

Calls

108 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(/ eps (pow (cos x) 2))
1.0ms	x	@	0	(/ 1 (* (cos (+ eps x)) (cos x)))
1.0ms	eps	@	0	(/ eps (pow (cos x) 2))
1.0ms	x	@	-inf	(/ 1 (* (cos (+ eps x)) (cos x)))
0.0ms	x	@	-inf	(+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3))

simplify199.0ms (1.4%)

Memory

16.9MiB live, 208.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 468×	`lower-fma.f64`
11 468×	`lower-fma.f32`
6 294×	`lower-*.f64`
6 294×	`lower-*.f32`
3 350×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	532	10018
1	1679	9762
2	5644	9566
0	8216	9186

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 419

Calls

Call 1

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

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

rewrite363.0ms (2.6%)

Memory

5.3MiB live, 240.6MiB allocated

Rules

4 786×	`lower-*.f32`
4 778×	`lower-*.f64`
4 496×	`lower-fma.f32`
4 486×	`lower-fma.f64`
2 318×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	714
0	100	710
1	493	539
2	4664	527
0	8129	497

Stop Event

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

Counts

20 → 429

Calls

Call 1

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

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

eval193.0ms (1.4%)

Memory: -24.5MiB live, 209.9MiB allocated
Compiler: Compiled 25 307 to 1 697 computations (93.3% saved)

prune190.0ms (1.4%)

Memory

1.4MiB live, 292.5MiB allocated

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	972	23	995
Fresh	5	2	7
Picked	3	2	5
Done	0	1	1
Total	980	28	1 008

Accuracy

100.0%

Counts

1 008 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (*.f64 (neg.f64 (cos.f64 x)) eps) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
✓	99.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	57.4%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (.f64 (.f64 (+.f64 (+.f64 x eps) x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x eps) x)))))
	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 eps))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
	98.6%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) (sin.f64 (+.f64 #s(literal 0 binary64) eps)))
▶	99.9%	(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x)))
	34.9%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 eps eps))))
	55.2%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 eps))))
▶	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
▶	98.7%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
	98.1%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) eps))
	98.7%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
▶	98.5%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))

Compiler

Compiled 1 038 to 554 computations (46.6% saved)

simplify149.0ms (1.1%)

Memory

7.3MiB live, 162.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
cost-diff	128	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
cost-diff	0	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
cost-diff	0	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) eps eps)
cost-diff	0	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
cost-diff	0	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
cost-diff	704	(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x)))

Rules

11 690×	`lower-fma.f32`
11 684×	`lower-fma.f64`
3 000×	`lower--.f64`
3 000×	`lower--.f32`
2 570×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	276
0	64	278
1	104	268
2	158	256
3	267	256
4	614	256
5	1810	256
6	5428	256
0	8197	249

Stop Event

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

Calls

Call 1

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

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

localize113.0ms (0.8%)

Memory

-5.1MiB live, 192.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
accuracy	0.015625	(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))
accuracy	0	(cos.f64 (+.f64 x x))
accuracy	0.00390625	(/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
accuracy	0.0234375	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
accuracy	0.00390625	(/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
accuracy	0.0078125	(fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64))
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
accuracy	0.8006845529987638	#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	0	(fma.f64 (*.f64 x x) eps eps)
accuracy	0	(*.f64 x x)
accuracy	0.4745618093409555	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
accuracy	0.9227288180468125	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
accuracy	0.01171875	(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x)))
accuracy	0.05097464160568397	(cos.f64 (+.f64 x eps))

Samples

71.0ms	249×	0	valid
3.0ms	7×	1	valid

Compiler

Compiled 207 to 38 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 15.0ms (28.6% of total)

ival-div: 10.0ms (19.1% of total)

ival-add: 8.0ms (15.3% of total)

ival-cos: 7.0ms (13.4% of total)

const: 4.0ms (7.6% of total)

ival-sin: 3.0ms (5.7% of total)

ival-pow2: 2.0ms (3.8% of total)

adjust: 1.0ms (1.9% of total)

ival-sub: 1.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.2%)

Memory

3.7MiB live, 42.0MiB allocated

Counts

22 → 420

Calls

Call 1

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

Outputs
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.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 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<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 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<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 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (+ eps x)))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ eps (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
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#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 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/3 (pow x 2)) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/3 (pow x 2)) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/3 (pow x 2)) 1) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/3 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/3 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/3 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/3 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2))) (taylor 0 x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (* 2 x)) (taylor inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (neg (* -2 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (neg (* -2 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (neg (* -2 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (cos (neg (* -2 x))) (taylor -inf x) (#s(alt (cos.f64 (+.f64 x x)) (patch (cos.f64 (+.f64 x x)) #<representation binary64>) () ())) ())

Calls

105 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(/ eps (+ 1/2 (* 1/2 (cos (+ x x)))))
3.0ms	x	@	-inf	(/ eps (+ 1/2 (* 1/2 (cos (+ x x)))))
1.0ms	eps	@	inf	(/ eps (+ 1/2 (* 1/2 (cos (+ x x)))))
1.0ms	eps	@	0	(+ (* (* x x) eps) eps)
1.0ms	eps	@	-inf	(* (/ 1 (cos (+ x eps))) (/ (sin eps) (cos x)))

simplify245.0ms (1.8%)

Memory

24.4MiB live, 172.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 132×	`lower-fma.f64`
13 132×	`lower-fma.f32`
6 148×	`lower-*.f64`
6 148×	`lower-*.f32`
4 942×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	351	4680
1	1016	4545
2	2972	4403
0	8399	4196

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 409

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

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* 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)))
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(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (*.f64 (sin.f64 eps) (-.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 (neg.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 eps))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(fma.f64 (neg.f64 (sin.f64 eps)) x (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (cos.f64 eps)))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+.f64 (fma.f64 (neg.f64 (sin.f64 eps)) x (.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (cos.f64 eps))) (.f64 (.f64 (.f64 (*.f64 x (sin.f64 eps)) #s(literal 2/3 binary64)) x) x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(*.f64 (cos.f64 x) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (.f64 (neg.f64 (cos.f64 x)) eps) (sin.f64 x) (.f64 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) eps) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
-1
#s(literal -1 binary64)
(- (* 1/3 (pow x 2)) 1)
(fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* 1/3 (pow x 2)) 1)
(fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* 1/3 (pow x 2)) 1)
(fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* (pow x 2) (- 1/3 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/3 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/3 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* (pow x 2) (- 1/3 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/3 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 1/3 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) (.f64 x x) #s(literal -2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -4/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal -2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(cos (* 2 x))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(cos (* 2 x))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(cos (* 2 x))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(cos (* 2 x))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(cos (neg (* -2 x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))

rewrite276.0ms (2%)

Memory

-24.2MiB live, 248.4MiB allocated

Rules

4 428×	`lower-*.f32`
4 420×	`lower-*.f64`
4 270×	`lower-/.f32`
4 260×	`lower-/.f64`
3 996×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	239
0	64	241
1	279	213
2	1876	213
0	8820	213

Stop Event

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

Counts

22 → 556

Calls

Call 1

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

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

eval196.0ms (1.4%)

Memory: 0.4MiB live, 258.1MiB allocated
Compiler: Compiled 23 858 to 2 169 computations (90.9% saved)

prune198.0ms (1.4%)

Memory

-12.3MiB live, 314.1MiB allocated

Pruning

30 alts after pruning (24 fresh and 6 done)

	Pruned	Kept	Total
New	1 150	10	1 160
Fresh	6	14	20
Picked	2	3	5
Done	0	3	3
Total	1 158	30	1 188

Accuracy

100.0%

Counts

1 188 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.7%	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) #s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
	98.6%	(/.f64 (sin.f64 eps) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (cos.f64 (+.f64 x eps))))
	99.7%	(/.f64 #s(approx (sin eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
	99.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (*.f64 (neg.f64 (cos.f64 x)) eps) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)))
✓	99.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps))))
✓	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	57.4%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 (.f64 (.f64 (+.f64 (+.f64 x eps) x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x eps) x)))))
	99.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (sin.f64 eps))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (/.f64 #s(approx (sin eps) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (cos.f64 x)))
	99.7%	(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 eps) (cos.f64 x)))
	34.9%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 eps eps))))
	55.2%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 eps))))
	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
	98.4%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) #s(approx (* 1/2 (cos (+ x x))) (fma.f64 (neg.f64 x) x #s(literal 1/2 binary64))))))
	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
✓	98.7%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/3 binary64) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.4%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
	98.1%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps #s(approx (pow (cos x) 2) #s(approx (+ (* (+ (* (* x x) 1/3) -1) (* x x)) 1) #s(literal 1 binary64)))))
	99.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) eps))
	98.7%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
	98.6%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
✓	98.5%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
	6.3%	#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 x x) eps))))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (.f64 x x)))) eps eps))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (.f64 (.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))))

Compiler

Compiled 1 562 to 516 computations (67% saved)

regimes55.0ms (0.4%)

Memory

-4.6MiB live, 114.5MiB allocated

Counts

62 → 1

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
16.0ms	eps
15.0ms	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)

regimes40.0ms (0.3%)

Memory

10.6MiB live, 90.7MiB allocated

Counts

43 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	x
13.0ms	eps
11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes34.0ms (0.2%)

Memory

-2.4MiB live, 76.3MiB allocated

Counts

40 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms	x
10.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes30.0ms (0.2%)

Memory

16.8MiB live, 56.2MiB allocated

Counts

36 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	eps
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes28.0ms (0.2%)

Memory

-1.7MiB live, 40.8MiB allocated

Counts

33 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes41.0ms (0.3%)

Memory

-9.5MiB live, 29.6MiB allocated

Counts

31 → 1

Calls

Call 1

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

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

Calls

3 calls:

23.0ms	eps
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

-20.6MiB live, 18.7MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

17.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	x
5.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.2%)

Memory

-18.6MiB live, 18.0MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

16.0ms	eps
3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

9.7MiB live, 9.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify13.0ms (0.1%)

Memory

-39.5MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	442
1	136	442

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.6s (11.3%)

Memory

25.7MiB live, 1 207.7MiB allocated

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
13 218×	`lower-fma.f64`
13 218×	`lower-fma.f32`
13 132×	`lower-fma.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
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	41	239
0	64	241
1	279	213
2	1876	213
0	8820	213
0	532	10018
1	1679	9762
2	5644	9566
0	8216	9186
0	61	487
0	113	472
1	505	369
2	4635	369
0	8175	353
0	709	11463
1	2285	11197
2	7608	11093
0	8838	10702
0	72	714
0	100	710
1	493	539
2	4664	527
0	8129	497
0	351	4680
1	1016	4545
2	2972	4403
0	8399	4196

Stop Event

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

Compiler

Compiled 922 to 460 computations (50.1% saved)

preprocess202.0ms (1.5%)

Memory: -4.1MiB live, 203.3MiB allocated
Compiler: Compiled 448 to 154 computations (65.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze45.0ms (0.3%)

sample6.7s (48.7%)

explain132.0ms (1%)

preprocess22.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify55.0ms (0.4%)

localize36.0ms (0.3%)

series11.0ms (0.1%)

simplify300.0ms (2.2%)

rewrite219.0ms (1.6%)

eval51.0ms (0.4%)

prune58.0ms (0.4%)

simplify177.0ms (1.3%)

localize281.0ms (2%)

series101.0ms (0.7%)

simplify259.0ms (1.9%)

rewrite216.0ms (1.6%)

eval258.0ms (1.9%)

prune162.0ms (1.2%)

simplify148.0ms (1.1%)

localize244.0ms (1.8%)

series51.0ms (0.4%)

simplify199.0ms (1.4%)

rewrite363.0ms (2.6%)

eval193.0ms (1.4%)

prune190.0ms (1.4%)

simplify149.0ms (1.1%)

localize113.0ms (0.8%)

series31.0ms (0.2%)

simplify245.0ms (1.8%)

rewrite276.0ms (2%)

eval196.0ms (1.4%)

prune198.0ms (1.4%)

regimes55.0ms (0.4%)

regimes40.0ms (0.3%)

regimes34.0ms (0.2%)

regimes30.0ms (0.2%)

regimes28.0ms (0.2%)

regimes41.0ms (0.3%)

regimes19.0ms (0.1%)

regimes17.0ms (0.1%)

regimes27.0ms (0.2%)

regimes12.0ms (0.1%)

regimes24.0ms (0.2%)

regimes7.0ms (0%)

regimes4.0ms (0%)

simplify13.0ms (0.1%)

soundness1.6s (11.3%)

preprocess202.0ms (1.5%)

end0.0ms (0%)

Profiling

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

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